Gauge invariance of parametrized systems and path integral quantization

Details Gauge invariance of parametrized systems and path integral quantization Gauge invariance of parametrized systems and path integral quantization

2001-08-30

arxiv.org/abs/gr-qc/0108079v1

Int.J.Mod.Phys. A14 (1999) 5105-5120

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages

Scientific paper

10.1142/S0217751X99002414

Gauge invariance of systems whose Hamilton-Jacobi equation is separable is improved by adding surface terms to the action fuctional. The general form of these terms is given for some complete solutions of the Hamilton-Jacobi equation. The procedure is applied to the relativistic particle and toy universes, which are quantized by imposing canonical gauge conditions in the path integral; in the case of empty models, we first quantize the parametrized system called ``ideal clock'', and then we examine the possibility of obtaining the amplitude for the minisuperspaces by matching them with the ideal clock. The relation existing between the geometrical properties of the constraint surface and the variables identifying the quantum states in the path integral is discussed.

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