Author
Christopher C. Bernido
Bio: Christopher C. Bernido is an academic researcher. The author has contributed to research in topics: Functional integration & Propagator. The author has an hindex of 1, co-authored 1 publications receiving 42 citations.
Papers
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TL;DR: In this article, the Aharonov-Bohm effect is formulated in terms of a constrained path integral, which is explicitly evaluated in the covering space of the physical background to express the propagator as a sum of partial propagators corresponding to homotopically different paths.
Abstract: The Aharonov–Bohm effect is formulated in terms of a constrained path integral. The path integral is explicitly evaluated in the covering space of the physical background to express the propagator as a sum of partial propagators corresponding to homotopically different paths. The interference terms are also calculated for an infinitely thin solenoid, which are found to contain the usual flux dependent shift as the dominant observable effect and an additional topological shift unnoticeable in the two slit interference experiment.
43 citations
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TL;DR: In this paper, path integral formulations for the Smorodinsky-Winternitz potentials in two-and three-dimensional Euclidean space are presented, where path integral evaluations explicitly in terms of the propagators and the spectral expansions into the wave-functions are discussed.
Abstract: Path integral formulations for the Smorodinsky-Winternitz potentials in two- and three-dimensional Euclidean space are presented. We mention all coordinate systems which separate the Smorodinsky-Winternitz potentials and state the corresponding path integral formulations. Whereas in many coordinate systems an explicit path integral formulation is not possible, we list in all soluble cases the path integral evaluations explicitly in terms of the propagators and the spectral expansions into the wave-functions.
136 citations
TL;DR: In this article, the interaction of point particles in a gauge theory for gravity in 2 + 1 dimensions with particular emphasis on the effects of spin is analyzed, and it is shown that the known space-time solution for spinning sources in Einstein gravity exhibits torsion at the location of the sources.
126 citations
TL;DR: In this paper, an exact path integral treatment of the hydrogen atom was proposed based on the bijective transformation of Kustaanheimo and Stiefel, which reduced the radial path integral for the hydrogen atoms into that for an oscillator in R 3 by one-to-one mapping.
56 citations
TL;DR: In this article, the motion of a nonrelativistic charged particle in a plane, multiply-connected region is studied within the framework of Feynman's pathintegral approach to quantum mechanics.
Abstract: The motion of a nonrelativistic charged particle in a plane, multiply-connected region is studied within the framework of Feynman's path-integral approach to quantum mechanics. In particular, the authors study the simple case when the multiply-connected region is obtained by excluding a disc from the plane. If a nonzero magnetic flux is confined inside the disc, this is shown to include a change in the one-dimensional unitary representation of the fundamental group of the space which enters a proper definition of the path-integral. In this way, a simple explanation of the Aharonov-Bohm effect is shown to arise.
39 citations
TL;DR: In this article, the authors evaluate the quantum propagator for systems with boundaries and topological constraints using the Streit-Hida formulation where the Feynman path integral is realized in the framework of white noise analysis.
Abstract: Using the Streit–Hida formulation where the Feynman path integral is realized in the framework of white noise analysis, we evaluate the quantum propagator for systems with boundaries and topological constraints. In particular, the Feynman integrand is given as generalized white noise functionals for systems with flat wall boundaries and periodic constraints. Under a suitable Gauss–Fourier transform of these functionals the quantum propagator is obtained for: (a) the infinite wall potential; (b) a particle in a box; (c) a particle constrained to move in a circle; and (d) the Aharonov–Bohm system. The energy spectrum and eigenfunctions are obtained in all four cases.
24 citations