States and Observables in Hamiltonian Semiclassical Scalar Electrodynamics

TL;DR

This paper discusses the foundational concepts and structures of semiclassical scalar electrodynamics across various gauges, focusing on states, observables, and symmetry transformations, and introduces a bundle framework for these semiclassical states.

Contribution

It formulates axioms for semiclassical scalar electrodynamics and introduces a semiclassical bundle structure to describe states and symmetries across different gauges.

Findings

Semiclassical states can be viewed as classical backgrounds with quantum states in external fields.

Axiomatic formulation of semiclassical properties in scalar electrodynamics.

Semiclassical bundle structure unifies classical and quantum descriptions across gauges.

Abstract

The main notions of semiclassical scalar electrodynamics in different gauges (Hamiltonian, Couloumb, Lorentz) are discussed. These are semiclassical states, Poincare transformations, fields, observables, gauge equivalence. General properties of these objects are formulated as axioms of semiclassical theory; they are heuristically justified. In particular, a semiclassical state may be viewed as a set of classical background field and quantum state in the external background. Superpositions of these "elementary" states can be also considered. Set of all "elementary" semiclassical states forms a semiclassical bundle, with base being classical space and fibres being quantum states in the external background. Quantum symetry transformations (Poincare and gauge transformations) are viewed semiclassically as automorphisms of the semiclassical bundle. Specific features of electrodynamics are investigated for different gauges.