Canonical quantization of the relativistic particle in static spacetimes

Abstract

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 Schrödinger 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.

Revtex, 9 pages

References in corpus (4)

• Quantization of Spinning Particle with Anomalous Magnetic Momentum
• Quantization of a relativistic particle on the SL(2,R) manifold based on Hamiltonian reduction
• Quantization of systems with time-dependent constraints. Example of relativistic particle in plane wave
• Pseudoclassical Model of Spinning Particle with Anomalous Magnetic Momentum

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