TL;DR
This paper explores the symmetry properties of semiclassical approximations in quantum mechanics, focusing on Lie group invariance, and discusses conditions for reconstructing group transformations relevant to quantum field theory.
Contribution
It introduces an abstract framework for semiclassical mechanics emphasizing symmetry properties and provides conditions for reconstructing semiclassical group transformations.
Findings
Identifies axioms for semiclassical mechanics based on symmetry.
Derives conditions for reconstructing semiclassical group transformations.
Discusses implications for Poincare invariance and quantum anomalies.
Abstract
Essential properties of semiclassical approximation for quantum mechanics are viewed as axioms of an abstract semiclassical mechanics. Its symmetry properties are discussed. Semiclassical systems being invariant under Lie groups are considered. An infinitesimal analog of group relation is written. Sufficient conditions for reconstructing semiclassical group transformations (integrability of representation of Lie algebra) are discussed. The obtained results may be used for mathematical proof of Poincare invariance of semiclasical Hamiltonian field theory and for investigation of quantum anomalies.
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