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Register a new userCovariant Quantization of CPT-violating Photons
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We perform the covariant canonical quantization of the CPT- and Lorentz-symmetry-violating photon sector of the minimal Standard-Model Extension, which contains a general (timelike, lightlike, or spacelike) fixed background tensor $k_{AF}^mu$. Well-known stability issues, arising from complex-valued energy states, are solved by introducing a small photon mass, orders of magnitude below current experimental bounds. We explicitly construct a covariant basis of polarization vectors, in which the photon field can be expanded. We proceed to derive the Feynman propagator and show that the theory is microcausal. Despite the occurrence of negative energies and vacuum-Cherenkov radiation, we do not find any runaway stability issues, because the energy remains bounded from below. An important observation is that the ordering of the roots of the dispersion relations is the same in any observer frame, which allows for a frame-independent condition that selects the correct branch of the dispersion relation. This turns out to be critical for the consistency of the quantization. To our knowledge, this is the first system for which quantization has consistently been performed, in spite of the fact that the theory contains negative energies in some observer frames.
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We present a consistent, generally covariant quantization of light for non-vacuum birefringent, Lorentz-symmetry breaking electrodynamics in the context of the Standard Model Extension. We find that the number of light quanta in the field is not frame independent, and that the interaction of the quantized field with matter is necessarily birefringent. We also show that the conventional Lorenz gauge condition used to restrict the photon-mode basis to solutions of the Maxwell equations must be weakened to consistently describe Lorentz symmetry violation.
The source of CPT-violation in the photon sector of the Standard Model Extension arises from a Chern-Simons-like contribution that involves a coupling to a fixed background vector field $k_{AF}^mu$. These Lorentz- and CPT-violating photons have well-known theoretical issues that arise from missing states at low momenta when $k_{AF}^mu$ is timelike. In order to make the theory consistent, a tiny mass for the photon can be introduced, well below current experimental bounds. The implementation of canonical quantization can then be implemented as in the CPT-preserving case by using the Stuckelberg mechanism. We explicitly construct a covariant basis of properly-normalized polarization vectors at fixed three-momentum satisfying the momentum space field equations, in terms of which the vector field can be expanded. As an application of the theory, we calculate the Cherenkov radiation rate for the case of purely timelike $k_{AF}^mu$, and find a radiation rate at high energies that has a contribution that does not depend on the mass used to regulate the photons.
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