Canonical quantization of the relativistic particle in static spacetimes

Details Canonical quantization of the relativistic particle in static spacetimes Canonical quantization of the relativistic particle in static spacetimes

1996-01-15

arxiv.org/abs/gr-qc/9601022v1

Class.Quant.Grav.13:553-558,1996

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Revtex, 9 pages

Scientific paper

10.1088/0264-9381/13/3/018

We perform the canonical quantization of a relativistic spinless particle moving in a curved and static spacetime. We show that the classical theory already describes at the same time both particle and antiparticle. The analyses involves time-depending constraints and we are able to construct the two-particle Hilbert space. The requirement of a static spacetime is necessary in order to have a well defined Schr\"odinger equation and to avoid problems with vacuum instabilities. The severe ordering ambiguities we found are in essence the same ones of the well known non-relativistic case.

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