Photon as a Vector Goldstone Boson: Nonlinear $σ$ Model for QED

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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Four pages, latex, no figures; references added and minor changes in the text

Scientific paper

We show that QED in the Coulomb gauge can be considered as a low energy linear approximation of a non-linear $\sigma $-type model where the photon emerges as a vector Goldstone boson related to the spontaneous breakdown of Lorentz symmetry down to its spatial rotation subgroup at some high scale $M$. Starting with a general massive vector field theory one naturally arrives at this model if the pure spin-1 value for the vector field $A_{\mu}(x)$ provided by the Lorentz condition $\partial_{\mu}A_{\mu}(x)=0$ is required. The model coincides with conventional QED in the Coulomb gauge in the limit of M going to infinity and generates a very particular form for the Lorentz and CPT symmetry breaking terms, which are suppressed by powers of $M$.

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