Poincare Invariance of Hamiltonian Semiclassical Field Theory

TL;DR

This paper rigorously proves Poincare invariance in Hamiltonian semiclassical field theory, introducing notions of semiclassical states and fields, and establishing their invariance properties within an axiomatic framework.

Contribution

It provides a mathematical proof of Poincare invariance for both elementary and composed semiclassical states and fields, advancing the theoretical foundation of semiclassical field theory.

Findings

Poincare invariance of semiclassical states is rigorously established.

Introduction of a notion of semiclassical field with proven invariance.

Degeneracy of inner product for composed states under certain conditions.

Abstract

Semiclassical Hamiltonian field theory is investigated from the axiomatic point of view. A notion of a semiclassical state is introduced. An "elementary" semiclassical state is specified by a set of classical field configuration and quantum state in this external field. "Composed" semiclassical states viewed as formal superpositions of "elementary" states are nontrivial only if the Maslov isotropic condition is satisfied; the inner product of "composed" semiclassical states is degenerate. The mathematical proof of Poincare invariance of semiclassical field theory is obtained for "elementary" and "composed" semiclassical states. The notion of semiclassical field is introduced; its Poincare invariance is also mathematically proved.