Q1. What are the contributions in this paper?
In this paper, the authors considered path integrals over trajectories in a plane ( with polar coordinates r and 0, 0 < r < oo, r < oo 0 < 0 < 2~ ) where the constraint could be expressed a s ǫ > 0.
On a path integral with a topological constraint
TL;DR: In this article, a method to evaluate a path integral with a topological constraint involving a point singularity in a plane is presented. And the path integration is performed explicitly in the universal covering space.
About: This article is published in Physics Letters A.The article was published on 1988-03-14 and is currently open access. It has received 7 citations till now. The article focuses on the topics: Constraint (information theory) & Functional integration.
Summary (1 min read)
Jump to: and [JoL mtm) 8mr2_J Jt,~]]
JoL mtm) 8mr2_J Jt,~]
- Here the quantity EQUATION is still a functional of the "radial" path, and the radial path integration has still to be performed.
- To perform the radial path integration the authors make use of the identity.
- The propagator expression obtained in (16) coincides with the corresponding expressions of refs. [ 2 ] and [ 3 ] , which shows that this method does indeed yield the correct results.
Did you find this useful? Give us your feedback
Citations
More filters
10 citations
TL;DR: In this paper, the formalism of path integrals in multiply connected spaces is applied to the problem of two anyons, and the problem is solved by a path integrator.
4 citations
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.
4 citations
TL;DR: In this article, the formalism of path integrals in multiply connected spaces is applied to the problem of two anyons, and the problem is solved by a path integrator.
Abstract: We apply the formalism of path integrals in multiply connected spaces to the problem of two anyons.
3 citations
TL;DR: In this article, the statistical properties of plane polymer loops enclosing a constant area were investigated, using a continuous model from the start, and an analytic expression for the generating functional was obtained, which in turn was used to derive the distribution function for the enclosed area, the average squared distance of a given repeating unit from the origin, and the entropic force on a repeating unit.
Abstract: The statistical mechanical properties of plane polymer loops enclosing a constant area are investigated, using a continuous model from the start. For this purpose an analytic expression for the generating functional is obtained, which in turn is used to derive (1) the distribution function for the enclosed area, (2) the average squared distance of a given repeating unit from the origin, and (3) the entropic force on a repeating unit.
3 citations
References
More filters
TL;DR: In this paper, the authors presented a simplification of the path integral solution of the Schrodinger equation in terms of coordinates which need not be Cartesian and discussed the relationship between the distance and time differentials.
Abstract: In this paper we present a simplification of the path integral solution of the Schrodinger equation in terms of coordinates which need not be Cartesian. After presenting the existing formula, we discuss the relationship between the distance and time differentials. Making this relationship precise through the technique of stationary phase, we are able to simplify the path integral. The resulting expression can be used to obtain a Hamiltonian path integral. Finally, we comment on a similar phenomenon involving differentials in the Ito integral.
136 citations
TL;DR: The status of exactly solvable problems within the path integral formulation of non-relativistic quantum mechanics is reviewed in this paper, where some applications of these exact results are presented.
131 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
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