Timeless path integral for relativistic quantum mechanics

Details Timeless path integral for relativistic quantum mechanics Timeless path integral for relativistic quantum mechanics

2010-09-28

arxiv.org/abs/1009.5436v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

30 pages

Scientific paper

Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all possible paths in the constraint surface specified by the (relativistic) Hamiltonian constraint, and each path contributes with a phase identical to the classical action divided by $\hbar$. The timeless path integral manifests the timeless feature as it is completely independent of the parametrization for paths. For the special case that the Hamiltonian constraint is a quadratic polynomial in momenta, the transition amplitude admits the timeless Feynman's path integral over the (relativistic) configuration space.

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