QED with external field: Hamiltonian treatment for anisotropic medium formed by the Lorentz-non-invariant vacuum

Abstract

Nonlinear electrodynamics, QED included, is considered against the Lorentz-noninvariant external field background, treated as an anisotropic medium. Hamiltonian formalism is applied to electromagnetic excitations over the background, and entities of electrodynamics of media, such as field inductions and intensities, are made sense of in terms of canonical variables. Both conserved and nonconserved generators of space-time translations and rotations are defined on the phase space, and their Hamiltonian equations of motion and Dirac bracket relations, different from the Poincaré algebra, are established. Nonsymmetric, but-in return-gauge-invariant, energy-momentum tensor suggests a canonical momentum density other than the Poynting vector. A photon magnetic moment is found to govern the evolution of the photon angular momentum. It is determined by the antisymmetric part of the energy-momentum tensor.

Lorentz-violating Euler-Heisenberg effective action

“…An interesting point about the decomposition of (k F ) µναβ (Eq. ( 35)), in terms of a symmetry tensor c µν , is that it is also found in the Born-Infeld electrodynamics, with an (Lorentz-violating) external field [33]. In particular, this decomposition restricts the Lorentz-violating electrodynamics to a nonbirefringence sector [34].…”

Nonlinear magnetic response of the magnetized vacuum to applied electric field

“…The situation remains simple, however, when we may disregard the anisotropy of the linear magnetic response. The inverse magnetic permeability tensor inherent in the second-rank polarization tensor ( 15) is, in the special frame, the constant tensor [21] µ…”

“…The constant background magnetic-like field makes an uniaxial medium in any of the special frames[21].…”

Axion-induced birefringence effects in laser driven nonlinear vacuum interaction

“…Most of them rely on the hypothetical photon-ALP oscillations driven by an external magnetic field [20][21][22][23][24]. This is because, on the one hand, the resulting axion effects manifest in the modification of the optical properties of the vacuum, i.e., birefringence and dichroism [25][26][27][28][29][30], whereas, on the other hand, the regeneration process of a photon from an ALP could also provide some trace of its existence [31][32][33][34]. Both ideas have been implemented in polarimetry [35][36][37][38] and "Light Shining Through a Wall" [39][40][41][42][43][44][45][46][47] experiments, but the feeble coupling between a photon and an ALP remains a big challenge to overcome in the search of high levels of sensitivity.…”