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Feynman-type integrals defined in terms of general cylindrical approximations

Jan Tarski

Springer eBooksApr 6, 20088 citations

THE PHASE SPACE FEYNMAN PATH INTEGRAL WITH GAUGE INVARIANCE AND ITS CONVERGENCE

Wataru Ichinose

Convergence of a time-slicing approximation is studied in a general way of the Feynman path integral in phase space with an electromagnetic potential. In the present paper a new approximation of the Feynman path integral in phase space, different from the familiar one in physics, is proposed so that its convergence can be shown independently of the choice of electromagnetic potentials and that gauge invariance of the Feynman path integral defined by its limit can be shown directly. It is also shown that the Feynman path integral in phase space defined above can be expressed in the form of the Feynman path integral in configuration space defined in the familiar way in physics, which Feynman himself stated heuristically.Convergence of a time-slicing approximation is studied in a general way of the Feynman path integral in phase space with an electromagnetic potential. In the present paper a new approximation of the Feynman path integral in phase space, different from the familiar one in physics, is proposed so that its convergence can be shown independently of the choice of electromagnetic potentials and that gauge invariance of the Feynman path integral defined by its limit can be shown directly. It is also shown that the Feynman path integral in phase space defined above can be expressed in the form of the Feynman path integral in configuration space defined in the familiar way in physics, which Feynman himself stated heuristically.

Reviews in Mathematical PhysicsNov 1, 200010 citations

Remarks on convergence of feynman path integrals

Daisuke Fujiwara

Springer eBooksJan 31, 200620 citations

On approximations of Feynman path integrals

Tapani Hyttinen

We study approximations of Feynman path integrals in finite dimensional spaces and how the approximations determine the propagator.

arXiv:2208.06206Aug 12, 20220 citations

More accurate discrete-time approximation of the Feynman path integral

Daniel R. Stump

A discrete-time approximation of the Feynman path integral is derived, for which the potential is approximated at each step by a quadratic polynomial; this is more accurate than the usual approximation for which the potential is approximated by a constant. This approximation is studied for several simple examples, by Monte Carlo calculations of the path integral.

Physical Review AJul 1, 19877 citations

Convergence of Feynman Path Integrals

Daisuke Fujiwara

Mathematical physics studiesJan 1, 20170 citations

On the cylindrical approximation of the feynman path integral

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