Avoiding gauge ambiguities in cavity quantum electrodynamics

Systems of interacting charges and fields are ubiquitous in physics. Recently, it has been shown that Hamiltonians derived using different gauges can yield different physical results when matter degrees of freedom are truncated to a few low-lying energy eigenstates. This effect is particularly prominent in the ultra-strong coupling regime. Such ambiguities arise because transformations reshuffle the partition between light and matter degrees of freedom and so level truncation is a gauge dependent approximation. To avoid this gauge ambiguity, we redefine the electromagnetic fields in terms of potentials for which the resulting canonical momenta and Hamiltonian are explicitly unchanged by the gauge choice of this theory. Instead the light/matter partition is assigned by the intuitive choice of separating an electric field between displacement and polarisation contributions. This approach is an attractive choice in typical cavity quantum electrodynamics situations.

NOTE ON AN ACTION FOR A PARTICLE IN THE HOŘAVA–LIFSHITZ GRAVITY

We classify a recently proposed action for a free particle which is compatible with Hořava–Lifshitz gravity, and then obtain the subluminal and the superluminal limits without gauge ambiguity in terms of Hamiltonian formulation.

Hamiltonian formulations of Yang–Mills theory and gauge ambiguity in quantization

A general formulation of the Hamiltonian in non-Abelian Yang–Mills theory is given. The subject of gauge-fixing ambiguity is investigated. It is shown how this type of degeneracy affects the Faddeev–Popov prescription for the corresponding path-integral formulation at the quantum level. A method for treating this problem is developed. The ideas are implemented by quantizing the theory in the axial gauge. PACS Nos.: 11.10Ef, 11.15-q, 11.15Tk

Euclidean Thermal Green Functions of Photons in Generalized Euclidean Rindler Spaces for Any Feynman-Like Gauge

The thermal Euclidean Green functions for Photons propagating in the Rindler wedge are computed by employing an Euclidean approach within any covariant Feynman-like gauge. This is done by generalizing a formula which holds in the Minkowskian case. The coincidence of the found (β = 2π)-Green functions and the corresponding Minkowskian vacuum Green functions is discussed in relation to the remaining static gauge ambiguity already found in previous works. Further generalizations to more complicated manifolds are discussed. Ward identities are verified in the general case.