References

1

G. Parisi and N. Sourlas, Phys.Rev.Lett. 43, 744 (1979); Nucl.Phys. B206, 321 (1982);
M.V. Feigel'man and A.M. Tsvelik, Sov.Phys. JETP, 56, 823 (1982); Phys.Lett. 95A, 469 (1983);
For a comprehensive review see J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (2nd Edition, Clarendon Press, Oxford, 1993).

2

H. Ezawa and J. R. Klauder, Prog.Thor.Phys. 74, 104 (1985);
L.P. Singh and F. Steiner, Phys.Lett. 166B, 155 (1986);
H. Nakazato, K. Okano, L. Schülke and Y. Yamahaka, Nucl.Phys. B346, 611 (1990).

3

C.W. Gardiner, Handbook of Stochastic Methods (Springer Series in Synergetics, Vol. 13, Springer, Berlin, 1983).

4

H. Kleinert, Path Integrals in Quantum Mechanics, Statistics and Polymer Physics, World Scientific, Second Edition, 1995.

5

In Section 10.5 of Ref. [4] it is shown that the correct time slicing of an interaction in a path integral is of the midpoint type, corresponding to a=1/2. Sometimes this is referred to as the midpoint prescription for defining the sliced action, but it can actually be derived from the short-time action along a classical orbit.

6

A. Pais and G.E. Uhlenbeck, Phys. Rev. 79, 145 (1950);
M.V. Ostrogradsky, Mem. Acad. Sci. St-Petersburg, 6, 385 (1850); See also: E.T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge University Press, Cambridge, 1959);
and Section 17.3 in Vol. II of H. Kleinert, Gauge Fields in Condensed Matter, (World Scientific, Singapore, 1989).

7

M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, 1992).

8

J.R. Klauder, Ann. Phys. (NY), 188, 120 (1988).