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- Number and annihilation/creation formalism for bosons (under commutation) and for fermions (under anti-commutation) is derived for objects in the orbit ##X^+_m##. However, photons are not represented by this orbit of the Poincare group. As a result, how can the resulting formalism be utilized for photons? (See for example, Folland, Quantum Field Theory: A Tourist Guide for Mathematicians, https://bookstore.ams.org/view?ProductCode=SURV/149)
The Hilbert space for the derivation is:
##\mathcal{H}=L^2(X_m^+,\lambda)##
where λ denotes the invariant measure over ##X_m^+##.
This space does not include photons because they are not represented by the orbit ##X_m^{+}##.
Thus, it would seem that the resulting derivation would not apply to photons which are bosons.
##\mathcal{H}=L^2(X_m^+,\lambda)##
where λ denotes the invariant measure over ##X_m^+##.
This space does not include photons because they are not represented by the orbit ##X_m^{+}##.
Thus, it would seem that the resulting derivation would not apply to photons which are bosons.
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