Gupta-Bleuler’s quantization of a parity-odd CPT -even electrodynamics of the standard model extension

Abstract

Following a successfully quantization scheme previously developed in Ref.[1] for a parity-even gauge sector of the SME, we have established the Gupta-Bleuler quantization of a parity-odd and CPT-even electrodynamics of the standard model extension (SME) without recoursing to a small photon mass regulator. Keeping the photons massless, we have adopted the gauge fixing condition: G(Aµ) = (∂0 +κ 0j ∂j)(A0 +κ 0k A k )+∂iA i . The four polarization vectors of the gauge field are exactly determined by solving an eigenvalue problem, exhibiting birefringent second order contributions in the Lorentz-violating parameters. They allow to express the Hamiltonian in terms of annihilation and creation operators whose positivity is guaranteed by imposing a weak Gupta-Bleuler constraint, defining the physical states. Consequently, we compute the field commutation relation which has been expressed in terms of Pauli-Jordan functions modified by Lorentz violation whose light-cone structures have allowed to analyze the microcausality issue.

A perfectly conducting surface in electrodynamics with Lorentz symmetry breaking

“…Possible effects of Lorentz symmetry violation have been investigated in many contexts, for example, the Casimir effect [8][9][10][11], QED [12][13][14][15][16], hydrogen atom [17,18], noncommutative field theories [19][20][21], space-times with a non-trivial topology [22], gravity theory [23][24][25][26][27][28], electromagnetic wave propagation [29][30][31][32], studies of photon field quantization [33][34][35], effects on the classical electrodynamics [36][37][38][39][40][41], among others.…”

Fermion Scattering in a CPT-Even Lorentz Violation Quantum Electrodynamics

“…A modified proposal of an LV gauge condition yielding a satisfactory covariant quantization of the electromagnetic field (in the absence of photon mass) was recently developed [21,22]. This is an alternative route to some gauge fixing relations defined in the presence of a small photon mass [45,46].…”

“…Aspects about the covariant quantization of the LV quantum electrodynamics were recently addressed and analyzed [20], including a small photon mass factor. An alternative analysis keeping the photon massless but considering a modified gauge fixing was also performed [21,22].…”

Field Sources in a CPT-Even Lorentz-Violation Maxwell Electrodynamics

“…The photon sector of the SME has been extensively investigated in literature. We can mention, for instance, the vacuum emission of Cherenkov radiation [13][14][15], modifications on the Casimir effect [16,17], studies con-cerning the radiative generation of the CFJ term [18][19][20][21][22], modifications in the dispersion relations [23][24][25][26][27][28][29][30][31], effects on the classical electrodynamics [32][33][34][35][36], effects induced in the hydrogen atom [37], the photon field quantization [38][39][40], effects of Aharonov-Bohm type [41][42][43] and so on.…”