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Prog. Theor. Phys. Vol. 56 No. 4 (1976) pp. 1318-1335

An Operator Formalism to the Path Integral Method

Tetsuo Gotō and Sigefumi Naka^*

Department of Physics and Atomic Energy Research Institute, College of Science and Engineering, Nihon University, Kanda, Tokyo
^*Institute for Nuclear Study, University of Tokyo, Tanashi, Tokyo

(Received April 7, 1976)

Abstract:

An operator formalism to the path integral method is developed. In this formalism the operator characterizing the trajectories of the particle is introduced and the usual path integral is expressed in terms of expectation value of a functional of that operator. We also investigate the Wiener-Hermite expansion on the basis of our operator formalism. Feynman's path integral is justified as a sort of analytic continuation of the path integral in the Wiener process.

URL : http://ptp.ipap.jp/link?PTP/56/1318/
DOI : 10.1143/PTP.56.1318

[ Full Text PDF : FREE ACCESS (1004K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. R. P. Feynman, Rev. Mod. Phys. 20 (1948), 367[APS].
   R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
2. E. Paley and N. Wiener, Fourier-transforms in the complex domain (Amer. Math. Soc. Colloquium Publications XIX, 1930).
3. R. H. Cameron, J. Math. and Phys. 39 (1960), 126.
   E. Nelson, J. Math. Phys. 5 (1964), 332[CrossRef].
4. De Witt-Morette, C. Commun. Math. Phys. 28 (1972), 47[CrossRef].
   De Witt-Morette, C. Commun. Math. Phys. 37 (1974), 63[CrossRef].
5. A. Katz, Classical Mechanics, Quantum Mechanics, Field Theory (Academic Press, New York & London, 1965).
6. I. M. Gelfand and A. M. Yaglom, J. Math. Phys. 1 (1960), 48[CrossRef].
7. M. Kac, Proceedings of Second Berkeley Symposium on Mathematical Statistics and Probability, (Univ. of California Press. 1951), 189.
   M. Kac, Probability and related topics in physical sciences (Interscience Publishers, Inc., New York, 1959), Chap. IV.
8. H. Ezawa, J. R. Klauder and L. A. Shepp, Ann. of Phys. 88 (1974),588[CrossRef].
9. N. Wiener, Nonlinear Problem in Random Theory (John Wiley & Son's Inc., New York, 1958).
   T. Imamura, W. C. Meecham and A. Siegel, J. Math. Phys. 6 (1965), 695[CrossRef].
10. R. H. Cameron and W. T. Martin, Duke Math. J. 12 (1945, a), 489.
11. G. Rosen, Formulation of Classical and Quantum Dynamical Theory (Academic Press, 1969), 118.

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 60 No. 5 (1978) pp. 1298-1303 :

   Formal Solution of Fokker-Planck Equation in the Operator Approach

   Tetsuo Gotō

2. Progress of Theoretical Physics Vol. 62 No. 1 (1979) pp. 278-292 :

   Canonical Approach to Spinning Particles

   Shigefumi Naka

3. Progress of Theoretical Physics Vol. 78 No. 2 (1987) pp. 423-434 :

   Ordinary Time Stochastic Quantization of Bosonic String and Its Supersymmetric Effective Action

   Toshio Sakamoto

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