Constraint quantization of parametrized relativistic gauge systems in curved spacetimes

Journal Article · Thu Feb 15 04:00:00 EST 1990 · Physical Review, D (Particles Fields); (USA)

OSTI ID:6962968

Hajriaacek, P ^[1]; Kuchar, K V ^[2]

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1. Institut fuer Theoretische Physik der Universitaet Bern, CH-3012 Bern, Switzerland (CH)
2. Department of Physics, University of Utah, Salt Lake City, Utah 84112 (USA)

The Dirac constraint quantization of a finite-dimensional relativistic gauge system with a quadratic super-Hamiltonian and linear supermomenta is investigated as a model for quantizing generally covariant field theories (such as the Einstein theory of gravitation). It is shown that the constraints can be geometrically factor ordered in such a way that their commutators do not produce more constraints. The ensuing quantum theory is invariant under all relevant transformations of the classical theory (point transformations in phase space, mixing of the supermomentum constraints, their adjoinment to the super-Hamiltonian, and scaling of the super-Hamiltonian). Moreover, it yields the same results---namely, the Klein-Gordon equation and the associated (indefinite) inner product---as those obtained by first eliminating the gauge degrees of freedom and then quantizing the ensuing physical theory.

• OSTI ID: 6962968
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 41:4; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EQUATIONS
FIELD THEORIES
FUNCTIONS
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
GRAVITATION
HAMILTONIANS
INVARIANCE PRINCIPLES
KLEIN-GORDON EQUATION
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
QUANTIZATION
QUANTUM OPERATORS
RELATIVITY THEORY
SPACE
SPACE-TIME
STRUCTURE FUNCTIONS
WAVE EQUATIONS