Sum-Over-Histories Quantization of Relativistic Particle

Details Sum-Over-Histories Quantization of Relativistic Particle Sum-Over-Histories Quantization of Relativistic Particle

2000-11-22

arxiv.org/abs/gr-qc/0011077v1

Class.Quant.Grav. 21 (2004) 1519-1558

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

47 pages, 3 figures, LaTeX2e

Scientific paper

10.1088/0264-9381/21/6/017

Sum-over-histories quantization of particle-like theory in curved space is discussed. It is reviewed that the propagator satisfies the Schrodinger equation respective wave equation with a Laplace-like operator. The exact dependence of the operator on the choice of measure is shown. Next, modifications needed for a manifold with a boundary are introduced, and the exact form of the equation for the propagator is derived. It is shown that the Laplace-like operator contains some distributional terms localized on the boundary. These terms induce proper boundary conditions for the propagator. This choice of boundary conditions is explained as a consequence of a measurement of particles on the boundary. The interaction with sources inside of the domain and sources on the boundary is also discussed.

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