Transversal affine connection and quantization of constrained systems
Journal Article
·
· Journal of Mathematical Physics (New York); (USA)
- Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland (CH)
- Department of Physics, University of Utah, Salt Lake City, Utah 84112 (USA)
The Dirac quantization of a finite-dimensional relativistic system with a quadratic super-Hamiltonian and linear supermomenta is investigated. In a previous work, the operator constraints were consistently factor-ordered in such a way that the resulting quantum theory was invariant under all relevant transformations of the classical theory. The method was based on a special choice of coordinates and gauge. Here, coordinate-independent methods are worked out and a quite general gauge is used. A new mathematical concept, the so-called transversal affine connection,'' is introduced. This connection is not a {ital linear} connection and is associated with a {ital degenerate} metric. The corresponding curvature tensor is defined and its components are calculated. The formalism is used to reconstruct the operator constraints, clarify their geometric meaning, and calculate their commutators.
- OSTI ID:
- 6802807
- Journal Information:
- Journal of Mathematical Physics (New York); (USA), Journal Name: Journal of Mathematical Physics (New York); (USA) Vol. 31:7; ISSN JMAPA; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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