Abstract:The problem of propagation of photons and massive vector mesons in the presence of Lorenz and CPT invariance violating medium is studied when the parity-odd medium is bounded by a hyperplane separating it from the vacuum. The solutions in both half-spaces are carefully discussed and in the case of space-like boundary stitched on the boundary with help of the Bogolubov transformations provided by the space-like ChernSimons vector. The presence of two different Fock vacua is shown and the probability amplitude for transmission of particles from vacuum to parity breaking medium is calculated. We have also found classical solutions and showed that the results are consistent with ones obtained by canonical quantization formalism. In the cases, both of entrance to and of escaping from parity-odd medium, the probabilities for reflecting and passing through were found for each polarization using the classical solutions. Finally, the propagator for each polarization is obtained in the momentum space. Boundary effects under consideration are of certain importance for registration of local parity violation in the finite volume of heavy ion fireball and/or of a star with cold axion condensate.

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The transition between a Minkowski space region and a parity breaking medium domain is thoroughly discussed. The requirement of continuity of the field operator content across the separating boundary of the two domains leads to Bogolyubov transformations, squeezed pairs states and squeeze operators that turn out to generate a functional SU(2) algebra. According to this algebraic approach, the reflection and transmission probability amplitude across the separating boundary are computed. The probability rate of the emission or absorption of squeezed pairs out of the vacuum (generalization of the Sauter-Schwinger-Nikishov formula) is obtained.

In this work we consider how the appearance of gradients of pseudoscalar condensates in dense systems may possibly influence the transport properties of photons in such a medium as well as other thermodynamic characteristics. We adopt the hypothesis that in regions where the pseudoscalar density gradient is large the properties of photons and fermions are governed by the usual lagrangian extended with a Chern-Simons interaction for photons and a constant axial field for fermions. We find that these new pieces in the lagrangian produce non-trivial reflection coefficients both for photons and fermions when entering or leaving a region where the pseudoscalar has a non-zero gradient. A varying pseudoscalar density may also lead to instability of some fermion and boson modes and modify some properties of the Fermi sea. We speculate that some of these modifications could influence the cooling rate of stellar matter (for instance in compact stars) and have other observable consequences. While quantitative results may depend on the precise astrophysical details most of the consequences are quite universal and consideration should be given to this possibility.

The electrodynamics supplemented with a Chern-Simons (CS) action (Carrol-Field-Jackiw electrodynamics) in a half space is studied. The passage of photons and massive vector mesons through a boundary between the CS medium and the vacuum of conventional Maxwell electrodynamics is investigated. Effects of reflection from a boundary (up to the total one) are revealed when vector particles escape to vacuum and income from vacuum passing the boundary.