Schrödinger type equation associated with the Lévy and Volterra Laplacians | Zendy

Kazuyoshi Sakabe | Zendy

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Schrödinger type equation associated with the Lévy and Volterra Laplacians

Author(s) -

Kazuyoshi Sakabe

Publication year - 2007

Publication title -

communications on stochastic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.224

H-Index - 10

eISSN - 2688-6669

pISSN - 0973-9599

DOI - 10.31390/cosa.1.3.06

Subject(s) - volterra equations , type (biology) , volterra integral equation , mathematics , mathematical physics , mathematical analysis , physics , integral equation , nonlinear system , quantum mechanics , geology , paleontology

In this paper, we discuss the application of white noise analysis to the Feynman path integral in the fleld theory. By introducing normal coordinates which permit us to describe the system as a set of independent harmonic oscillators, we calculate the Feynman path integral using white noise functionals. Moreover, we give an inflnite dimensional Schrodinger type equation associated with the Land Volterra Laplacians by introducing new renormalizations of the integral.

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