Institute of Theoretical Physics · Faculty of Mathematics and Physics, Charles University
Class. Quantum Grav. 21, 1519-1557 (2004)
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.
@article{UTF53,
author = {Krtouš, P},
title = {{Sum-over-histories quantization of relativistic particle}},
journal = {Class. Quantum Grav.},
volume = {21},
pages = {1519-1557},
year = {2004},
eprint = {gr-qc/0011077},
archivePrefix = {arXiv},
}