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Prog. Theor. Phys. Vol. 64 No. 6 (1980) pp. 2164-2178

On the Ordering Independence of the Path Integral Formalism

Tarō Kashiwa

Department of Physics, Kyushu University 33, Fukuoka 812

(Received March 21, 1980)

Abstract:

It is shown that a path integral expression of the generating functional is independent of the ordering scheme one employs. The essential point is that {(G_l,l-G_l,l-1)-(G_l-1,l-G_l-1,l-1)}/ Δt is not of order Δt but of order unity, where G_j,k is the propagator.
We also discuss the case of fermion and obtain the same conclusion.
Thus one may choose any ordering scheme suitable for the problem under consideration even in the path integral formalism.

URL : http://ptp.ipap.jp/link?PTP/64/2164/
DOI : 10.1143/PTP.64.2164

[ Full Text PDF : FREE ACCESS (865K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 73 No. 3 (1985) pp. 762-789 :

   Lattice Fermion and σ-Model

   Tarō Kashiwa and Hiroto So

2. 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

3. 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

4. Progress of Theoretical Physics Vol. 95 No. 2 (1996) pp. 421-431 :

   A General Form of the Constraints in the Path Integral Formula

   Taro Kashiwa

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