Renormalization of Poincare Transformations in Hamiltonian Semiclassical Field Theory

TL;DR

This paper rigorously analyzes the Poincare invariance of semiclassical Hamiltonian field theory, introducing semiclassical states and fields, and proving their invariance properties within an axiomatic framework.

Contribution

It introduces a formal notion of semiclassical states and fields, and provides a mathematical proof of their Poincare invariance in Hamiltonian semiclassical field theory.

Findings

Semiclassical states are characterized by classical configurations and quantum states.

Composed semiclassical states require Maslov isotropic condition for nontriviality.

Poincare invariance is rigorously proven for both elementary and composed states.

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.