On the Generalization of the Duru-Kleinert-Propagator Transformations

Pelster, Axel; Wunderlin, A.

doi:10.4028/www.scientific.net/msf.123-125.685

Cited by 6 publications

(19 citation statements)

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“…In order to avoid unnecessary overlap I do not repeat the space-time transformation technique as sketched in [1], e.g [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], and references therein. For the actual formulation of the path integral representations of the potentials I use the canonical path integral definition as developed in [20-23, 27, 35, 36].…”

Section: Introductionmentioning

confidence: 99%

Conditionally solvable path integral problems

Grosche¹

1995

J. Phys. A: Math. Gen.

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Abstract. New classes of exactly solvable potentials are discussed within the path integral formalism. They are constructed from the hypergeometric and confluent Natanzon potentials, respectively. It is found that they allow incorporation of four free parameters, which give rise to fractional power behaviour, long-range and strongly anharmonic terms. We find six different classes of such potentials.

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Section: Introductionmentioning

confidence: 99%

Conditionally solvable path integral problems

Grosche¹

1995

J. Phys. A: Math. Gen.

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“…The above variational treatment of the action is still somewhat complicated and calls for a simpler procedure which was found recently [16]. Let us vary the paths q µ (t) in the usual holonomic way, i.e., with fixed endpoints, and consider the associated variations δx i = e i µ (q)δq µ of the Cartesian coordinates.…”

Section: Alternative Formulation Of Action Principle With Torsionmentioning

confidence: 99%

“…It is the purpose of these lectures to demonstrate the power of the new quantum equivalence principle and to discuss its consequences also at the classical level, where the familiar action principle breaks down and requires an important modification [12,15,16]. The geometric reason for this lies in the fact that infinitesimal variations can no longer be taken as closed curves; they possess a defect analogous to the Burgers vector in crystal physics.…”

Section: Introductionmentioning

confidence: 99%

Quantum Equivalence Principle

Kleinert

1997

NATO ASI Series

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A simple mapping procedure is presented by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed directly into those in curved space with torsion. Our procedure evolved from well-established methods in the theory of plastic deformations, where crystals with defects are described mathematically as images of ideal crystals under active nonholonomic coordinate transformations. Our mapping procedure may be viewed as a natural extension of Einstein's famous equivalence principle. When applied to time-sliced path integrals, it gives rise to a new quantum equivalence principle which determines short-time action and measure of fluctuating orbits in spaces with curvature and torsion. The nonholonomic transformations possess a nontrivial Jacobian in the path integral measure which produces in a curved space an additional term proportional to the curvature scalar R, thus canceling a similar term found earlier by DeWitt. This cancelation is important for correctly describing semiclassically and quantum mechanically various systems such as the hydrogen atom, a particle on the surface of a sphere, and a spinning top. It is also indispensable for the process of bosonization, by which Fermi particles are redescribed by those fields.

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“…Whereas the transformed potential V (h(q, t)) may have a convenient form when expressed in the new coordinate q, the kinetic term m 2 h ′ 2q 2 is in general nasty, and the term linear inq also cannot be seen as of practical use. To achieve a more convenient form of the path integral (7) I proceed in two steps, first, the term proportional toq is gauged away, second, a time-transformation is performed ( [13][14][15][16][17][18][19], in particular Refs. [18,19], and c.f.…”

Section: Explicitly Time-dependent Duru-kleinert Transformationmentioning

confidence: 99%

“…To achieve a more convenient form of the path integral (7) I proceed in two steps, first, the term proportional toq is gauged away, second, a time-transformation is performed ( [13][14][15][16][17][18][19], in particular Refs. [18,19], and c.f. [19] for a comprehensive but slightly different discussion)…”

Section: Explicitly Time-dependent Duru-kleinert Transformationmentioning

confidence: 99%

Path integral solution of a class of explicitly time-dependent potentials

Grosche

1993

Physics Letters A

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A specific class of explicitly time-dependent potentials is studied by means of path integrals. For this purpose a general formalism to treat explicitly time-dependent space-time transformations in path integrals is sketched. An explicit time-dependent model under consideration is of the form V (q, t) = V [q/ζ(t)]/ζ 2 (t), where V is a usual potential, and ζ(t) = (at 2 + 2bt + c) 1/2 . A recent result of Dodonov et al. for calculating corresponding propagators is incorporated into the path integral formalism by performing a space-time transformation. Some examples illustrate the formalism.

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On the Generalization of the Duru-Kleinert-Propagator Transformations

Cited by 6 publications

References 0 publications

Conditionally solvable path integral problems

Conditionally solvable path integral problems

Quantum Equivalence Principle

Path integral solution of a class of explicitly time-dependent potentials

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