On evaluating topologically constrained path integrals
TL;DR: Another method is presented where the quantum correction term, ∝ (ħ/8 Mr 2 ) d t , arises naturally in carrying out the constrained path integration.
About: This article is published in Physics Letters A.The article was published on 1989-04-10. It has received 4 citations till now. The article focuses on the topics: Singular point of a curve & Path integral formulation.
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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
TL;DR: In this paper, the Green function for a relativistic particle interacting with a gravitational point source and a flux confined at the origin of the ( rho, phi )-space is evaluated using Feynman's summation-over-histories.
Abstract: The Green function for a relativistic particle interacting with a gravitational point source and a flux confined at the origin of the ( rho , phi )-space is evaluated using Feynman's summation-over-histories. The bound state energy spectrum is calculated when a uniform magnetic field is applied perpendicular to the ( rho , phi )-space.
6 citations
TL;DR: Explicit path integration in a space with a ring-shaped topological defect using toroidal coordinates is carried out in this article, where the toroidal Aharonov-Bohm experiment is taken as an example.
Abstract: Explicit path integration is carried out in a space with a ring-shaped topological defect using toroidal coordinates. The toroidal Aharonov-Bohm experiment is taken as an example.
3 citations
TL;DR: In this paper, the path integral evaluation for a particle moving in spacetimes with topological defects is presented, and the systems discussed are: (a) a gravitational anyon, (b) a straight cosmic string, and (c) a ring-shaped topological defect.
1 citations
References
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TL;DR: In this article, it was shown that there exist effects of potentials on charged particles, even in the region where all the fields (and therefore the forces on the particles) vanish.
Abstract: In this paper, we discuss some interesting properties of the electromagnetic potentials in the quantum domain. We shall show that, contrary to the conclusions of classical mechanics, there exist effects of potentials on charged particles, even in the region where all the fields (and therefore the forces on the particles) vanish. We shall then discuss possible experiments to test these conclusions; and, finally, we shall suggest further possible developments in the interpretation of the potentials.
5,553 citations
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01 Jan 1986
TL;DR: In this article, the authors present an elementary account on the Wiener path integral as applied to Brownian motion, and the author progresses on to the statistics of polymers and polymer entanglements.
Abstract: This monograph distills material prepared by the author for class lectures, conferences and research seminars. It fills in a much-felt gap between the older and original work by Feynman and Hibbs and the more recent and advanced volume by Schulman.After presenting an elementary account on the Wiener path integral as applied to Brownian motion, the author progresses on to the statistics of polymers and polymer entanglements. The next three chapters provide an introduction to quantum statistical physics with emphasis on the conceptual understanding of many-variable systems. A chapter on the renormalization group provides material for starting on research work. The final chapter contains an over view of the role of path integrals in recent developments in physics. A good bibliography is provided for each chapter.
241 citations
TL;DR: In this article, the use of polar coordinates is examined in performing summation over all Feynman histories, and several relationships for the Lagrangian path integral and the Hamiltonians path integral are derived in the central force problem.
Abstract: Use of polar coordinates is examined in performing summation over all Feynman histories. Several relationships for the Lagrangian path integral and the Hamiltonian path integral are derived in the central‐force problem. Applications are made for a harmonic oscillator, a charged particle in a uniform magnetic field, a particle in an inverse‐square potential, and a rigid rotator. Transformations from Cartesian to polar coordinates in path integrals are rather different from those in ordinary calculus and this complicates evaluation of path integrals in polars. However, it is observed that for systems of central symmetry use of polars is often advantageous over Cartesians.
202 citations
TL;DR: In this article, exact propagators for a time-dependent harmonic oscillator with and without an inverse quadratic potential have been evaluated, and it is shown that these propagators depend only on the solutions of the classical unperturbed oscillator.
Abstract: By using Feynman’s definition of a path integral, exact propagators for a time−dependent harmonic oscillator with and without an inverse quadratic potential have been evaluated. It is shown that these propagators depend only on the solutions of the classical unperturbed oscillator. The relations between these propagators, the invariants, and the Schrodinger equation are also discussed.
114 citations
TL;DR: In this paper, the path integral for a string entangled around a singular point in two dimensions is evaluated in polar coordinates and applications are made for the entangled polymers with and without interactions, the Aharonov-Bohm effect and the angular momentum projection of a spinning top.
Abstract: Path integrals with a periodic constraint ∫θ ds =Θ+2πn (n=integer) are studied. In particular, the path integral for a string entangled around a singular point in two dimensions is evaluated in polar coordinates. Applications are made for the entangled polymers with and without interactions, the Aharonov–Bohm effect, and the angular momentum projection of a spinning top.
51 citations