The Feynman path integral for constrained systems
type: Item
instance of: scholarly article
title: The Feynman path integral for constrained systems
zbMATH Open document ID: 0731.58015
DOI: 10.1016/0003-4916(91)90021-Y
author: Steven K. Blau
published in: Annals of Physics
publication date: 1991-01-01T00:00:00Z
review text: The paper under review discusses how to construct a path integral representation of the propagator for a canonically quantized constrained system. Given a classical Lagrangian expressed in terms of an overdetermined set of coordinates one determines the classical Hamiltonian H and constraints \(\phi_ a\). In the canonical quantization they are promoted to the quantum Hamiltonian \({\mathfrak H}\) and constraint operators \(\phi_ a\) such that \({\mathfrak H}\) acts on a restricted Hilbert space consisting of the states \(| \psi >\) satisfying \(\phi_ a| \psi >=0\). Then reexpressing the Hamiltonian as a Weyl-ordered function of an ``effective'' momentum and position operators appropriate to this Hilbert space, one obtains a phase space path integral representation for the propagator \(\exp [-i(t'-t){\mathfrak H}]\) on these states. The ``effective'' Hamiltonian appearing in this path integral differs from the original classical Hamiltonian H. For related problems see also \textit{S. V. Shabanov}, J. Phys. A, Math. Gen. 24, No.6, 1199-1214 (1991; see the review above).
reviewed by: Takashi Ichinose
Mathematics Subject Classification ID: 58D30
Mathematics Subject Classification ID: 81S40
Mathematics Subject Classification ID: 81S30
zbMATH DE Number: 4209123
zbMATH Keywords: Feynman path integral
zbMATH Keywords: quantization for constrained systems
MaRDI profile type: Publication
cites work: On the Analogy Between Classical and Quantum Mechanics
cites work: Space-Time Approach to Non-Relativistic Quantum Mechanics
cites work: Q5569065
cites work: Q3740608
cites work: Path integrals in polar coordinates
cites work: Measure for measure: Covariant skeletonizations of phase space path integrals for systems moving on Riemannian manifolds
cites work: Quantization of relativistic systems with constraints
full work available at URL: 0003-4916(91)90021-y
OpenAlex ID: W2011687802
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description: scientific article; zbMATH DE number 4209123