Kaluza-Klein-like analysis of the configuration space of gauge theories

Journal Article · Tue Nov 15 04:00:00 EST 1994 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.50.6569· OSTI ID:6949091

Epp, R J ^[1]

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1. Physics Department, University of Winnipeg, Winnipeg, Manitoba, R3B2E9 (Canada)

It is well known that Dirac quantization of gauge theories is not, in general, equivalent to reduced quantization. When both approaches are self-consistent some additional criterion must be found in order to decide which approach is more natural, or correct. Now, in most cases quantization on the physical degrees of freedom is properly curved-space quantization, with a curvature that is neither constant nor Ricci flat. In a series of two papers, this being the first, we show that, unlike reduced quantization, Dirac quantization (acting in the physical Hilbert space) corresponds in a natural way to such a curved-space quantization scheme, and has remarkable similarities with other curved-space quantization schemes proposed elsewhere. We begin here with an in-depth analysis of the geometry of the classical configuration space of gauge theories. In particular, the existence of a metric on the full configuration space establishes a Yang-Mills connection with respect to the orbits---we emphasize the importance of this connection, as well as the condition the gauge theory must satisfy in order to define it. We also discuss, in Kaluza-Klein-like fashion, three Levi-Civita connections, their associated Ricci tensors, and interrelationships among them.

• OSTI ID: 6949091
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 50:10; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

661100 -- Classical & Quantum Mechanics-- (1992-)
662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BANACH SPACE
DEGREES OF FREEDOM
FIELD THEORIES
GEOMETRY
HILBERT SPACE
KALUZA-KLEIN THEORY
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MATHEMATICS
PARTICLE MODELS
QUANTIZATION
SPACE
UNIFIED GAUGE MODELS
UNIFIED-FIELD THEORIES