An algebraic approach to the quantization of constrained systems: Finite dimensional examples. [general relativity]

Thesis/Dissertation · Wed Jan 01 04:00:00 EST 1992

OSTI ID:7264502

Tate, R S

General relativity has two features in particular which make it difficult to apply to it existing schemes for the quantization of constrained systems. First, there is no background structure in the theory, which could be used, e.g., to regularize constraint operators, to identify a [open quotes]time[close quotes] or to define an inner product on physical states. Second, in the Ashtekar formulation of general relativity, which is a promising avenue to quantum gravity, the natural variables for quantization are not canonical; and, classically, there are algebraic identities between them. Existing schemes are usually not concerned with such identities. Thus, from the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a general prescription for finding the physical inner product, and is flexible enough to accomodate non-canonical variables. In this dissertation the author presents an algebraic formulation of the Dirac approach to the quantization of constrained systems. The Dirac quantization program is augmented by a general principle to find the inner product on physical states. Essentially, the Hermiticity conditions on physical operators determine this inner product. The author also clarifies the role in quantum theory of possible algebraic identities between the elementary variables. He uses this approach to quantize various finite dimensional systems. Some of these models test the new aspects of the algebraic framework. Others bear qualitative similarities to general relativity, and may give some insight into the pitfalls lurking in quantum gravity. The previous quantizations of one such model had many surprising features. When this model is quantized using the algebraic program, there is no longer any unexpected behaviour. The author also constructs the complete quantum theory for a previously unsolved relativistic cosmology.

• Research Organization: Syracuse Univ., NY (United States)
• OSTI ID: 7264502
• Country of Publication: United States
• Language: English

Related Subjects

661310* -- Relativity & Gravitation-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
FIELD THEORIES
GENERAL RELATIVITY THEORY
MATHEMATICS
QUANTIZATION
QUANTUM FIELD THEORY
QUANTUM GRAVITY