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Prog. Theor. Phys. Vol. 58 No. 4 (1977) pp. 1262-1270

Operator Ordering and Perturbation Expansion in the Path Integral Formalism

Masa-aki Sato

College of General Education, Osaka University, Toyonaka 560

(Received December 6, 1976)

Abstract:

The operator ordering problem in the path integral formalism is studied in the context of the perturbation expansion. For a given ordered Hamiltonian, there exists a path integral formula which reproduces the corresponding quantum mechanics, i.e., the same Feynman-Wick rules as the operator formalism. The Weyl ordering is shown to play an important role in connecting the discrete path integral (difined on a finite mesh) with the continuous one.

URL : http://ptp.ipap.jp/link?PTP/58/1262/
DOI : 10.1143/PTP.58.1262

[ Full Text PDF : FREE ACCESS (562K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. C. Garrod, Rev. Mod. Phys. 38 (1966), 483[APS].
2. J. -L. Gervais and A. Jevicki, Nucl. Phys. B 110 (1976), 93[CrossRef].
3. R. P. Feynman, Rev. Mod. Phys. 20 (1948), 267[APS].
   R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
4. M. Mizrahi, J. Math. Phys. 16 (1975), 2201[CrossRef].
5. See, for example, E. S. Abers and B. W. Lee, Phys. Rep. 9 (1973), 1[CrossRef].
6. F. A. Berezin, Theor. Math. Phys. 6 (1971), 194.

Citing Article(s) :

1. Journal of the Physical Society of Japan 61 (1992) pp. 55-63 :

   Path Integral Formulation of Curved Low Dimensional Space

   Shigeki Matsutani

2. Progress of Theoretical Physics Vol. 58 No. 6 (1977) pp. 1964-1972 :

   On the Path Integral in the Curved Space

   Toshiei Kimura

3. Progress of Theoretical Physics Vol. 64 No. 6 (1980) pp. 2164-2178 :

   On the Ordering Independence of the Path Integral Formalism

   Tarō Kashiwa

4. Progress of Theoretical Physics Vol. 80 No. 1 (1988) pp. 151-161 :

   Privileged Role of the Mid-Point Prescription in Path Integrations for Constrained Systems

   Hiroki Fukutaka and Taro kashiwa

5. Progress of Theoretical Physics Vol. 86 No. 2 (1991) pp. 575-579 :

   Operator Ordering in Stochastic Hamiltonian and Path Integral Formalism of Stochastic Quantization

   Nobuyuki Komoike

6. Progress of Theoretical Physics Vol. 88 No. 4 (1992) pp. 759-768 :

   Simple BRS Gauge-Fixing

   Ken-Iti Izawa

7. Progress of Theoretical Physics Vol. 92 No. 3 (1994) pp. 669-685 :

   Ordering, Symbols and Finite-Dimensional Approximations of Path Integrals

   Taro Kashiwa, Seiji Sakoda and Sergei V. Zenkin

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