Geometric quantization and constrained systems

Abhay Ashtekar, Matthew Stillerman

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

The problem of obtaining the quantum theory of systems with first class constraints is discussed in the context of geometric quantization. The precise structure needed on the constraint surface of the full phase space to obtain a polarization on the reduced phase space is displayed in a form that is particularly convenient for applications. For unconstrained systems, any polarization on the phase space leads to a mathematically consistent quantum description, although not all of these descriptions may be viable from a physical standpoint. It is pointed out that the situation is worse in the presence of constraints: a general polarization on the full phase space need not lead to even a mathematically consistent quantum theory. Examples are given to illustrate the general constructions as well as the subtle difficulties.

Original languageEnglish (US)
Pages (from-to)1319-1330
Number of pages12
JournalJournal of Mathematical Physics
Volume27
Issue number5
DOIs
StatePublished - Jan 1 1986

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Geometric Quantization
Constrained Systems
Phase Space
Polarization
Quantum Theory
quantum theory
polarization

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Ashtekar, Abhay ; Stillerman, Matthew. / Geometric quantization and constrained systems. In: Journal of Mathematical Physics. 1986 ; Vol. 27, No. 5. pp. 1319-1330.
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Geometric quantization and constrained systems. / Ashtekar, Abhay; Stillerman, Matthew.

In: Journal of Mathematical Physics, Vol. 27, No. 5, 01.01.1986, p. 1319-1330.

Research output: Contribution to journalArticle

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