Abstract
In this paper we work out the quantum mechanics of a free particle in genral metric from the functional point of view. We want to obtain ageneral coordinate transformations (GCT) covariant definition of the path integral. To this end we redefine the Δx on the time lattice so that the «velocity» Δx/Δt behaves as a GCT vector at the quantum level. The resulting Hamiltonian is the canonical one plus a term proportional to the scalar curvature, in agreement with DeWitt classical paper. The case of a vector potential interaction is also worked out.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
