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Sum-Over-Histories Quantization of Relativistic Particle

Pavel Krtous
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Abstract

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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Pavel Krtous. 2000-11-22. Sum-Over-Histories Quantization of Relativistic Particle. https://doi.org/10.1088/0264-9381%2F21%2F6%2F017

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