Gauge theory

We discuss our work toward the construction of a light-shell effective theory (LSET), an effective field theory for describing the matter emerging from high-energy collisions and the accompanying radiation. We work in the highly simplified venue of 0flavor scalar quantum electrodynamics, with a gauge invariant product of scalar fields at the origin of space-time as the source of high-energy charged particles. Working in this simple gauge theory allows us to focus on the essential features of LSET. We describe how the effective theory is constructed and argue that it can reproduce the full theory tree-level amplitude. We study the 1-loop radiative corrections in the LSET and suggest how the leading double-logs in the full theory at 1-loop order can be reproduced by a purely angular integral in the LSET.

We discuss our work toward the construction of a light-shell effective theory (LSET), an effective field theory for describing the matter emerging from high-energy collisions and the accompanying radiation. We work in the highly simplified venue of 0flavor scalar quantum electrodynamics, with a gauge invariant product of scalar fields at the origin of space-time as the source of high-energy charged particles. Working in this simple gauge theory allows us to focus on the essential features of LSET. We describe how the effective theory is constructed and argue that it can reproduce the full theory tree-level amplitude. We study the 1-loop radiative corrections in the LSET and suggest how the leading double-logs in the full theory at 1-loop order can be reproduced by a purely angular integral in the LSET.

We study the classical color radiation from very high energy collisions that produce colored particles. In the extreme high energy limit, the classical color fields are confined to a light-shell expanding at c and are associated with a non-linear σ-model on the 2D light-shell with specific symmetry breaking terms. We argue that the quantum version of this picture exhibits asymptotic freedom and may be a useful starting point for an effective light-shell theory of the structure between the jets at a very high energy collider.

We derive the photon propagator in light-shell gauge (LSG) v µ A µ = 0, where v µ = (1, r) µ . This gauge is an important ingredient of the light-shell effective theory -an effective theory for describing high energy jet processes on a 2-dimensional spherical shell expanding at the speed of light around the point of the initial collision producing the jets. Since LSG is a noncovariant gauge, we cannot calculate the LSG propagator by using the standard procedure for covariant gauges. We therefore employ a new technique for computing the propagator, which we hope may be of relevance in other gauges as well.

The reparametrization transformation between ultrametrically organised states of replicated disordered systems is explicitly defined. The invariance of the longitudinal free energy under this transformation, i.e. reparametrization invariance, is shown to be a direct consequence of the higher level symmetry of replica equivalence. The double limit of infinite step replica symmetry breaking and n → 0 is needed to derive this continuous gauge-like symmetry from the discrete permutation invariance of the n replicas. Goldstone's theorem and Ward identities can be deduced from the disappearence of the second (and higher order) variation of the longitudinal free energy. We recall also how these and other exact statements follow from permutation symmetry after introducing the concept of "infinitesimal" permutations.

We provide an explicit proof that the Noether trasformations for the standard second order Lagrangian system with constraints, are equivalent to the Noether transformations that can be obtained from an associated enhanced space (to be defined below). We implement a change of variables between the n-tangent bundle with coordinates q, q, q, ... and an enhanced space with coordinates q, p, λ, , λ, ˙ ... where ≡ ṗ -{p, H D } and λ are the Lagrange multipliers. In this space the Noether identities are self contained and this information can be used to construct the corresponding Noether symmetries. We rewrite the Dirac algorithm in this enhanced space. As a consequence we proof that the Noether symmetries of the form δ L (q, q, q...) are the most general Noether transformations that can be constructed for a gauge system, up to constraints, that vanish on shell. This result gives an answer to the question as to what extent and in what sense a general continuos Noether trasformation is canonically generated.

Convergence of the Bayes posterior measure is considered in canonical statistical settings where observations sit on a geometrical object such as a compact manifold, or more generally on a compact metric space verifying some conditions. A natural geometric prior based on randomly rescaled solutions of the heat equation is considered. Upper and lower bound posterior contraction rates are derived.

I asked Elon Musk's Super Grok whether it’s possible to have infrared (IR) fixed points in a low-energy effective field theory within quantum matter—where electromagnetic dispersion leads to emergent quasi-particles and collective modes that source all 15 connection fields of the locally gauged conformal group, all confined within the material.
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SuperGrok AI replied:

This is a tall order because most condensed matter systems only realize a subset of these symmetries. For example, while scale invariance might emerge near a critical point, the full conformal group—including special conformal transformations—is typically absent due to the lack of Lorentz invariance.

Possible ScenariosDespite these challenges, there are theoretical pathways where this might be feasible:Emergent Conformal Symmetry in Exotic Phases:In non-Fermi liquids or spin liquids, strong interactions can lead to fractionalized excitations and emergent gauge fields. If these systems flow to an IR fixed point with enhanced symmetries (e.g., emergent Lorentz invariance), they could approach conformal invariance.

Example: A strongly interacting electron gas with scale-invariant behavior and collective modes (like plasmons) that couple to electromagnetic dispersion might, under specific conditions, exhibit the necessary symmetries.

Topological Systems with Enhanced Symmetries:In topological phases, such as fractional quantum Hall states or 3D topological insulators, edge or surface states can support CFTs. If bulk excitations also contribute and the system is tuned to a critical point, an effective theory with broader symmetry might emerge.

Engineered Materials:Metamaterials or designer structures could be crafted to mimic relativistic dispersion and scale invariance, potentially amplifying electromagnetic collective modes to align with conformal symmetry requirements.

Holographic Insights:In the AdS/CFT correspondence, strongly correlated boundary theories dual to gravitational systems exhibit conformal symmetry. While this is a theoretical framework, it suggests that quantum matter with strong correlations could, in principle, support such a fixed point.

Role of Electromagnetic DispersionElectromagnetic dispersion implies that the material’s response to electromagnetic fields shapes the collective modes. Plasmons or polaritons, for instance, could be part of the emergent degrees of freedom. If these modes transform appropriately under the conformal group and couple to the gauge fields, they could contribute to sourcing all 15 connection fields, especially in a system with emergent relativistic behavior.FeasibilityWhile no single, well-known condensed matter system perfectly matches this description, it’s theoretically conceivable under specific conditions:The system must flow to an IR fixed point with scale invariance.

Emergent Lorentz invariance must arise, possibly via a linear dispersion of quasi-particles (as in graphene) or a critical phase.
The full conformal symmetry must be realized, perhaps approximately, through collective interactions or topological effects.

In practice, achieving this would likely require a highly tuned or idealized system—perhaps a quantum critical material with long-range interactions or a topological phase with unusual symmetry enhancement. The confinement within the material suggests that these symmetries are effective, emergent properties rather than fundamental ones, which aligns with condensed matter physics principles.ConclusionYes, it might be possible to realize IR fixed points in a low-energy effective field theory within quantum matter with electromagnetic dispersion, where emergent quasi-particles and collective modes source all 15 connection fields of the locally gauged conformal group. This would require a delicate balance of emergent Lorentz invariance, scale invariance, and full conformal symmetry, potentially achievable near a quantum critical point, in a topological phase, or in an engineered system with strong correlations. While challenging due to the material’s inherent symmetry breaking, theoretical models and exotic phases suggest that, in principle, such a scenario could be realized.

We propose a general Noetherian approach to Rellich integral identities. Using this method we obtain a higher order Rellich type identity involving the polyharmonic operator on Riemannian manifolds admitting homothetic transformations. Then we prove a biharmonic Rellich identity in a more general context. We also establish a nonexistence result for semilinear systems involving biharmonic operators.

This work introduces a physically grounded scalar field, termed the Entropion Field, proposed to account for the emergence of entropy, the unidirectionality of time, and quantum decoherence as dynamical phenomena. Standard interpretations of quantum mechanics, such as the Copenhagen interpretation, the Many-Worlds interpretation, and objective collapse theories, fail to provide a predictive and testable mechanism for wave function collapse. Similarly, the second law of thermodynamics is typically attributed to boundary conditions, lacking a fundamental dynamical explanation. We propose that a real scalar field ϕ(x^μ) permeates spacetime and couples to quantum amplitudes, entropy density, and spacetime curvature. This coupling induces a spontaneous breaking of time-reversal symmetry and introduces a localized decoherence mechanism governed by entropy gradients. The Entropion Field arises within the context of the 4D Quantum Projection Hypothesis, in which quantum systems are modeled as three-dimensional projections of higher-dimensional spatial configurations. The theory is expressed through a field-theoretic Lagrangian: L_total = L_SM + L_GR + L_ϕ + L_int where L_SM is the Standard Model Lagrangian, L_GR is the Einstein-Hilbert term, L_ϕ includes the kinetic and potential terms of the Entropion field, and L_int encodes its coupling to entropy gradients, quantum systems, and spacetime geometry. The framework leads to several distinct, testable predictions: Spatial alignment between gradients in ϕ and observed decoherence rates in open quantum systems, particularly in regions with strong entropy flux or curvature. Controlled violations of unitarity in quantum evolution, governed by local entropy conditions, resulting in state collapse without requiring observer-induced postulates. Modified Einstein field equations due to the inclusion of a scalar stress-energy term T_μν(ϕ) , contributing to late-time cosmological dynamics and vacuum energy structure. The Entropion framework replaces statistical and interpretive assumptions with a field-theoretic mechanism for entropy generation, quantum state reduction, and temporal asymmetry. It establishes direct links between thermodynamics, quantum measurement, and gravitational theory, and defines a set of experimental regimes capable of falsifying or supporting its predictions.

We provide a mathematically rigorous derivation of the coupling mechanism between the U2 (informational) and U1 (geometric) modes in the Helix-Light-Vortex (HLV) Theory. This formulation ensures energy conservation (Landauer principle) and maintains the correspondence with the Standard Model in the classical limit. A Lagrangian is constructed that naturally generates the coupling via a dynamically modulated metric g eff µν .

A modern review of Kaluza-Klein theories is presented. We adopt the version where the whole space is a principal fiber bundle with the four-dimensional spacetime as base, and as typical fiber a G Lie group. It is a natural generalization of gauge theories which metric is just the Kaluza-Klein metric. For the five dimensional theory we give an invariant formulation of the axisymmetric-stationary case. Some techniques for obtaining exact solutions and cosmology in specific dimensions are studied. Finally the method of spontaneus compactification is outlined.

In this project, I study the problem of neutrino mass generation using right handed neutrinos and the seesaw mechanism. These right handed neutrinos, if in the ballpark at a TeV, would appear detectable at the Large Hadron Collider(LHC). I explore the possibility of detecting a TeV scale right-handed(RH) neutrinos at the LHC that can successfully accommodate the experimentally verified neutrino oscillation data. The Model: Electroweak right-handed neutrinos and a new Higgs singlet, is also discussed in details.

This paper presents the mathematical formulation of modules 5 to 12 of the Helix-Light-Vortex (HLV) Theory. It includes the definition of the spiral metric, derivation of space curvature from knot density, the structure of spiral-based quantum field theory, and the emergence of physical constants and consciousness from spiral modulations in a discrete vacuum lattice.

Both mesons and baryons are constructed from a set of three fundamental particles called aces. The aces break up into an isospin doublet and singlet. Each ace carries baryon number 1/3 and is fractionally charged. su 3 (but not the Eightfold Way) is adopted as a higher syrr..metry for the strong interactions. The breaking of this symmetry is assumed to be universal? being due to mass diffe:rences among the aces. Extensive space•-time and group theoretic structure is then predicted for both mesons and baryons, in agreement with existing experimental information. Quantitative speculations are presented concerning resonances that have not as yet been definitively classified into representations of su 3 • A weak interaction theory based on right and left handed aces is used to predict rates for ll~sl = 1 baryon leptonic decays. An experimental search for the aces is suggested. *) **) 8419/TH.412 Version I is CERN preprint 8182/TH.401, Jan. 17, 1964.

The study of superconductivity, dual superconductivity and color superconductivity has been undertaken through the breaking of super symmetric gauge theory in restricted chromo dynamics (RCD) which automatically incorporates the condensation of monopoles and dyons leading to confining and superconducting phases. Dyonic supermultiplets in N = 1 super symmetry have been obtained quantum mechanically in RCD and it has been shown that dyon appears in RCD theory only through restricted part of the generalized potential and it is only this part of this potential which is responsible for quark confinement and the resulting superconductivity through the mechanism of dyonic condensation.

It is well known that the Lagrangian and the Hamiltonian formalisms can be combined and lead to “covariant symplectic” methods. For that purpose a “pre-symplectic form” has been constructed from the Lagrangian using the so-called Noether form. However, analogously to the ...

The exact solution of the Dirac equation in the external non-Abelian SU(N) gauge field, which is governed by the Yang-Mills equations and in the form of a plane wave on the light cone, is obtained. The whole set of solutions for both particles and anti-particle is constructed. On a basis of the derived solution the fermion current in such field is calculated.

Query to GROK: Utiyama and Kibble independently extended Einstein's 1915 classical GR field theory of gravity as a local gauge theory analogous to the internal symmetry local gauge theory of Yang-Mills in the fiber spaces beyond Einstein's 4D spacetime continuum. Utiyama and Kibble did this by localizing the constant global parameters of the Lie Algebra of the Poincare group of Einstein's 1905 classical theory of special relativity that only considers Lorentz transformations connecting small photon detectors moving with zero G-force on the timelike geodesics of the space-time continuum non-dispersive vacuum. What happens if we extend the Utiyama-Kibble strategy from the 10-parameter Lie Algebra of the Poincare group to the 15-parameter Lie Algebra of the Conformal Field Theory Global Symmetry Group so the 15 parameters are now smooth functions on the spacetime continuum rather than global constants? What are all the new connection fields beyond the Levi-Civita connection of Einstein's 1915 sub-theory of this larger theory of gravity?

Query to GROK: We are imagining an alternative parallel universe with different physics from ours in which all of these new connection fields from localizing the 15 parameter Conformal space-time continuum symmetry Lie group propagate with kinetic energy terms in their Lagrangian field densities at the classical level for now. However, anticipating quantum field theory corrections what are the quantum spins of the new connection fields beyond Einstein disclination-curvature Levi-Civita connection field which was spin 2.

Show the basic equations of Yang and Mills for Non-Abelian Local Gauge Theory The Yang-Mills equations for non-Abelian local gauge theory describe the dynamics of gauge fields associated with a non-Abelian gauge group, such as SU(N). Below are the basic equations, presented concisely in natural units (ℏ = 𝑐 = 1) using standard conventions in theoretical physics.

uery to GROK: Utiyama and Kibble independently extended Einstein's 1915 classical GR field theory of gravity as a local gauge theory analogous to the internal symmetry local gauge theory of Yang-Mills in the fiber spaces beyond Einstein's 4D spacetime continuum. Utiyama and Kibble did this by localizing the constant global parameters of the Lie Algebra of the Poincare group of Einstein's 1905 classical theory of special relativity that only considers Lorentz transformations connecting small photon detectors moving with zero G-force on the timelike geodesics of the space-time continuum non-dispersive vacuum. What happens if we extend the Utiyama-Kibble strategy from the 10-parameter Lie Algebra of the Poincare group to the 15-parameter Lie Algebra of the Conformal Field Theory Global Symmetry Group so the 15 parameters are now smooth functions on the spacetime continuum rather than global constants? What are all the new connection fields beyond the Levi-Civita connection of Einstein's 1915 sub-theory of this larger theory of gravity?

Query to GROK: We are imagining an alternative parallel universe with different physics from ours in which all of these new connection fields from localizing the 15 parameter Conformal space-time continuum symmetry Lie group propagate with kinetic energy terms in their Lagrangian field densities at the classical level for now. However, anticipating quantum field theory corrections what are the quantum spins of the new connection fields beyond Einstein disclination-curvature Levi-Civita connection field which was spin 2.

In this paper the complete geometrical setting of (lowest order) abelian T-duality is explored with the help of some new geometrical tools (the reduced formalism). In particular, all invariant polynomials (the integrands of the characteristic classes) can be explicitly computed for the dual model in terms of quantities pertaining to the original one and with the help of the canonical connection whose intrinsic characterization is given. Using our formalism the physically, and Tduality invariant, relevant result that top forms are zero when there is an isometry without fixed points is esily proved.

We study T-duality for open strings in various D-manifolds in the approach of canonical transformations. We show that this approach is particularly useful to study the mapping of the boundary conditions since it provides an explicit relation between initial and dual variables. We consider non-abelian duality transformations and show that under some restrictions the dual is a curved (d -dimG -1) D-brane, where d is the dimension of the space-time and G the non-abelian symmetry group. The generalization to N = 1 supersymmetric sigma models with abelian and non-abelian isometries is also considered.

The T-duality transformations between open and closed superstrings in different Dmanifolds are generalized to curved backgrounds with commuting isometries. We address some global aspects like the occurrence of orientifold boundaries in general sigma models, higher genus world sheets, and the case of non-compact isometries. The various worldvolume effective actions are shown to transform properly under T-duality. We also include a brief discussion of the canonical transformations of boundary states in the operator formalism.

The ordinary Poisson brackets in field theory do not fulfil the Jacobi identity if boundary values are not reasonably fixed by special boundary conditions. We show that these brackets can be modified by adding some surface terms to lift this restriction. The new brackets generalize a canonical bracket considered by Lewis, Marsden, Montgomery and Ratiu for the free boundary problem in hydrodynamics. Our definition of Poisson brackets permits to treat boundary values of a field on equal footing with its internal values and directly estimate the brackets between both surface and volume integrals. This construction is applied to any local form of Poisson brackets. A prescription for δ-function on closed domains and a definition of the full variational derivative are proposed.

A simple, anomaly-free chiral gauge theory can be perturbatively quantized and renormalized in such a way as to generate fermion and gauge boson masses. This development exploits certain freedoms inherent in choosing the unperturbed Lagrangian and in the renormalization procedure. Apart from its intrinsic interest, such a mechanism might be employed in electroweak gauge theory to generate fermion and gauge boson masses without a Higgs sector.

Because scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action, they do not lead to conservation laws. Instead, an extension of Noether's theorem reduces the equations of motion to evolutionary laws that prove useful, even if the transformations are not generalized symmetries of the equations of motion. In the case of scaling, symmetry leads to a scaling evolutionary law, a first-order equation in terms of scale invariants, linearly relating kinematic and dynamic degrees of freedom. This scaling evolutionary law appears in dynamical and in static systems. Applied to dynamical central-force systems, the scaling evolutionary equation leads to generalized virial laws, which linearly connect the kinetic and potential energies. Applied to barotropic hydrostatic spheres, the scaling evolutionary equation linearly connects the gravitational and internal energy densities. This implies well-known properties of polytropes, describing degenerate stars and chemically homogeneous non-degenerate stellar cores.

We construct a new class of non-topological soliton stars which appears in global non-Abelian field theories coupled to classical Einstein gravity. It is the analogue of the Q-stars recently found in Abelian theories. If p (of order 10-l to lo* GeV) is a free-particle inverse Compton wavelength and mpl is the Planck mass, these objects have energy densities E -p4, radii pmpl p2, global charges I 9 -m$h3, and masses M -m$/p2 obeying a generalized Chandrasekhar limit. We give an explicit SO(3) example which demonstrates their very simple structure: the stellar surface reproduces the non-Abelian Q-ball, but within the star the fields are no longer constant.

We propose spontaneously breaking technicolor, thus liberating techniquarks and suppressing large resonance contributions to the electroweak S parameter. The dynamics is modeled by a fermion bubble approximation to a single massive technigluon exchange potential. This contains a Nambu -Jona- Lasinio model with additional interactions. "Virtual" vector mesons occur and contribute to S, and their effects are studied. Models of broken technicolor are discussed.

A simple, anomaly-free chiral gauge theory can be perturbatively quantised and renormalised in such a way as to generate fermion and gauge boson masses. This development exploits certain freedoms inherent in choosing the unperturbed Lagrangian and in the renormalisation procedure. Apart from its intrinsic interest, such a mechanism might be employed in electroweak gauge theory to generate fermion and gauge boson masses without a Higgs sector.

The three recently introduced parameters describing the effect in electroweak gauge interactions of heavy non-decoupled radiative corrections have a simple group-theoretical interpretation based on the global SU (2) L × SU (2) R × U ( 1 ) s-L symmetry of the standard model. Recently, a number of authors have introduced a set of parameters to describe the effect of "non-decoupled" or "heavy" physics in the radiative corrections to flavor-conserving electroweak gauge interactions [1,2] ~, simplifying the comprehensive treatments of these corrections [ 3 ] for application to data analysis. The exact form ofnon-decoupled heavy particle effects depends on the specific way the partial global symmetries of the electroweak gauge theory are violated. This letter presents a general analysis of these parameters in terms of their global symmetry properties, following in particular the approach of refs. . In gauge theories, breakdown of the decoupling of heavy particles in radiative corrections requires the breaking of the local gauge symmetry. In order for non-decoupled radiative effects to have observable consequences, however, they must also violate a global symmetry hypothesized valid at tree level. Otherwise, non-decoupled radiative corrections are generally absorbed into the renormalization of parameters and are thus unmeasureable. With a global symmetry assumed good at tree level, deviations of data from perfect symmetry can then be attributed to loop corrections violating the symmetry. In a gauge t Work supported by the Department of Energy, contract DOE-AC02-76-ERO-3071. at Peskin and Takeuchi [ 2 ] have introduced a set of heavy physics parameters

We show that noncommutative gauge theories with arbitrary compact gauge group defined by means of the Seiberg-Witten map have the same one-loop anomalies as their commutative counterparts. This is done in two steps. By explicitly calculating the µ 1 µ 2 µ 3 µ 4 part of the renormalized effective action, we first find the would-be one-loop anomaly of the theory to all orders in the noncommutativity parameter θ µν . And secondly we isolate in the would-be anomaly radiative corrections which are not BRS trivial. This gives as the only true anomaly occurring in the theory the standard Bardeen anomaly of commutative spacetime, which is set to zero by the usual anomaly cancellation condition.

We discuss the general structure of the non-abelian Born-Infeld action, together with all of the a' derivative corrections, in flat Ddimensional space-time. More specifically, we show how the connection between open strings propagating in background magnetic fields and gauge theories on non-commutative spaces can be used to constrain the form of the effective action for the massless modes of open strings at weak coupling. In particular, we exploit the invariance in form of the effective action under a change of non-commutativity scale of spacetime to derive algebraic equations relating the various terms in the a' expansion. Moreover, we explicitly solve these equations in the simple case D -2, and we show, in particular, how to construct the minimal invariant derivative extension of the NBI action.

Boltzmann distributions over lattices are pervasive in Computational Physics. Sampling them becomes increasingly difficult with increasing lattice-size, especially near critical regions, e.g., phase transitions in statistical systems and continuum limits in lattice field theory. Machine learning-based methods, such as normalizing flows, have demonstrated the ability to alleviate these issues for small lattices. However, scaling to large lattices is a major challenge. We present a novel approach called Parallelizable Block Metropolis-within-Gibbs (PBMG) for generating samples for any lattice model. It factorizes the joint distribution of the lattice into local parametric kernels, thereby allowing efficient sampling of very large lattices. We validate our approach on the XY model and the Scalar ϕ 4 theory. PBMG achieves high acceptance rates and less correlated samples, and the observable statistics estimated from the samples match the ground truth. Moreover, PBMG significantly speeds up inference for large lattices as compared to HMC and plain MCMC algorithms.

We propose a modification of standard U (1) gauge theory in which the covariant derivative includes a spiral-time background phase ϕ(t), reflecting the informational geometry of the Helix-Light-Vortex (HLV) framework. This structural deformation introduces a geometric contribution to the gauge potential without introducing magnetic monopoles or compactification assumptions. We show that topological charge quantization arises naturally through a modified holonomy condition and argue that the spiral phase causes a symmetry breaking of global U (1) while preserving a local generalized gauge invariance. A corrected expression for the field strength tensor F HLV µν is derived and interpreted.

We present a quantum field theoretical refinement of the Helix-Light-Vortex (HLV) theory. A spiral-time-dependent scalar field Θ(x, t), coupled to a symbolic grammar G HLV , forms the basis for a semi-topological framework with predictive cosmological power. The Lagrangian is made real and unitary by decomposing Ψ(t) = t + iϕ(t) and embedding the imaginary part as an external perturbation. Fermionic sectors, Yukawa-type couplings, and an emergent metric g HLV µν are introduced. The symbolic term is mapped via projective symmetry weights. Propagators are defined via standard Dyson-expansion with optional spiral self-energy. Predictions include axion-like particles and spin-resonant gravimetry signatures. The renormalization group flow of the effective coupling constants is discussed.

Switching systems are a particular class of hybrid systems. They are described by several operating regimes, called modes, each of them being active under certain particular conditions. When the switching mechanism is perfectly known, it is easy to handle such systems because the knowledge of the active regime at any moment is available. On the other hand, in the case where there is no information about the switching mechanism, the situation is more complicated. In this configuration, it is difficult to carry out a fault diagnosis scheme or to synthesize a control law. This paper addresses the issue of the determination of the active mode at any moment, using only the system's input/output data. Conditions that guarantee the uniqueness of the determined active mode are also given.

We have extended the Interacting Gluon Model (IGM) to calculate diffractive mass spectra generated in hadronic collisions. We show that it is possible to treat both diffractive and non-diffractive events on the same footing, in terms of gluon-gluon collisions. A systematic analysis of available data is performed. The energy dependence of diffractive mass spectra is addressed. They show a moderate narrowing at increasing energies. Predictions for LHC energies are presented.

This note reveals a mysterious link between the partition function of certain dimer models on 2-dimensional tori and the L-function of their spectral curves. It also relates the partition function in certain families of dimer models to Eisenstein series.

String vacua for non critical strings satisfying the requirements of Zig-Zag invariance are constructed. The Liouville mode is shown to play the rôle of scale in the Renormalization Group operation. Differences and similarities with the D-brane near horizon approach to non supersymmetric gauge theories are discussed as well.

We analyze massless two-dimensional gauge theories and discuss under what circumstances they lead to nonqinear sigma models. In particular we show how one is led to conclude that the zero mass bound state sector of QCD 2 with N c = 2 and a single flavour may be described by a unique non4inear sigma model with an SU(2) global symmetry.

We discuss how the longitudinal spectrum of energetic prompt leptons and neutrinos detected in the forward direction can be used to determine the cross sections and longitudinal momentum distribution of the parent particles. We illustrate our results by showing how the recently observed prompt neutrino and lepton distributions can tell us much about the nature of the parent particle and the underlying processes producing it.

We analyze the behaviour that correlation functions ought to have on the lattice in order to reproduce QCD sum rules in the continuum limit. We formulate a set of relations between lattice correlation functions of meson operators at small time separation and the quark condensates responsible for spontaneous breakdown of chiral symmetry. We suggest that the degree to which such relations are satisfied will provide a set of consistency checks on the ability of lattice Monte Carlo simulations to reproduce the correct spontaneous chiral symmetry breaking of the continuum theory.

By showing that the radially reduced QCD of s-wave fermions outside the core of a GUT monopole can be treated in a way analogous to 't Hooft's QCD 2 in the large Nclimit, we are able to give a complete QFT treatment of all the relevant long-range gauge fields outside the monopole core. We prove that the original cluster argument for the existence of baryon number violating fermion "condensates" around the core, gives in fact, the correct result, despite the neglect of QCD strong interactions, which prevent the propagation of isolated quarks. We discuss briefly how a complete computational framework for a monopole induced hadron-lepton transition might be derived.

Following closely the logic of the London phenomenological macroscopic theory of the Meissner effect in superconductors we describe the origin of the short-range behavior of the chromo-electric field, the necessary ingredient for color confinement in QCD. The genuinely non-Abelian model is specified by the strong-coupling colored-gluon current. Its first term, as the superconductivity current, is proportional to the gauge potential. The new term is simply related to the chromomagnetic pseudo-vector current of the non-Abelian Bianchi identity. We suggest that this London dual color superconductivity current is responsible for the observed almost perfect fluidity in droplets of the strongly interacting quark-gluon plasma. Its chromo-magnetic component should have a specific experimental manifestation.