Path space measures for Dirac and Schr{umlt o}dinger equations: Nonstandard analytical approach

Journal Article · Fri Aug 01 04:00:00 EDT 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.532083· OSTI ID:526895

Nakamura, T ^[1]

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1. Sundai Preparatory School, 2-5-17, Kanda-Surugadai, Chiyoda-ku, Tokyo 101 (Japan)

A nonstandard path space {asterisk}-measure is constructed to justify the path integral formula for the Dirac equation in two-dimensional space{endash}time. A standard measure as well as a standard path integral is obtained from it. We also show that, even for the Schr{umlt o}dinger equation, for which there is no standard measure appropriate for a path integral, there exists a nonstandard measure to define a {asterisk}-path integral whose standard part agrees with the ordinary path integral as defined by a limit from time-slice approximant. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 526895
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 8 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
DIRAC EQUATION
FEYNMAN PATH INTEGRAL
SCHROEDINGER EQUATION
SPACE-TIME
TWO-DIMENSIONAL CALCULATIONS