Abstract
A definition of the Feynman path integral which does not rest on a limiting procedure based on time-slicing has been given by DeWitt-Morette. We present in this paper a discussion of real Gaussian measures and formulate expressions for the quantum statistical partition function directly in terms of measures of integration on the topological vector space ø0 of continuous functions defined on the time intervalT = (t a ,t b ), such thatx(t a ,t b )=0 for allx ɛ ø0. We give a definition of a measure for the space ø0 equivalent to the path integral based on the Uhlenbeck-Ornstein probability distribution. We give expressions for the partition function using the Wiener-Feynman measure and the Uhlenbeck-Ornstein measure. As an exercise in the use of the new techniques, we present calculations of moments of potential functions. The techniques will enable one to solve in a rigorous manner practical problems in quantum statistical mechanics.
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References
C. M. DeWitt,Commun. Math Phys. 28:47 (1972).
C. M. DeWitt, Preprint, Department of Astronomy and Center for Relativity Theory, University of Texas at Austin (1973).
R. F. Feynman and A. R. Hibbs,Quantum Mechanics and Path Integrals, McGraw Hill, New York (1965).
A. Seigel and T. Burke,J. Math. Phys. 13:1681 (1972).
A. Maheshwari and K. C. Sharma,Phys. Letters 46A:127 (1973).
I. M. Gelfand and A. M. Yaglom,J. Math. Phys. 1:48 (1960).
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Maheshwari, A. Functional integral representations of partition function without limiting procedure. Techniques of calculation of moments. J Stat Phys 12, 11–20 (1975). https://doi.org/10.1007/BF01024181
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DOI: https://doi.org/10.1007/BF01024181