Geodesic
The stochastic approach for non-hamiltonian systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 1, pp. 153-159 Cet article a éte moissonné depuis la source Math-Net.Ru

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The stochastic quantization of dissipative systems is discussed. It is shown that in order to stochastically quantize a system with dissipation, one has to restrict the Fourier transform of the space-time variable to the positive half domain in the complex plane. This breaks the time-reversal invariance, which manifests in the formulation through the resulting noninvariant forms for the propagators. The relation of the stochastic approach with the Caldeira and Leggett path-integral method is also analyzed. 
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R. Tzani. The stochastic approach for non-hamiltonian systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 1, pp. 153-159. http://geodesic.mathdoc.fr/item/TMF_1994_100_1_a14/

[1] V. Bargmann, E. P. Wigner, Proc. Nat. Acad. Sci. USA, 34 (1948), 211 | DOI | MR | Zbl

[2] V. P. Nair, R. Jackiw, Phys. Rev. D, 43 (1991), 1993 | DOI | MR

[3] L. P. S. Singh, C. R. Hagen, Phys. Rev. D, 9 (1974), 898 ; C. Fronsdal, Phys. Rev. D, 18 (1978), 3624 ; J. Fang, C. Fronsdal, Phys. Rev. D, 18 (1978), 3630 ; E. S. Fradkin, M. A. Vasiliev, Nucl. Phys., 291 (1987), 141 | DOI | DOI | DOI | DOI | MR

[4] W. Dittrich, M. Renter, Classical and Quantum Dynamics: from Classical Path to Path-Integral, Springer, Berlin, 1992 | MR | Zbl

[5] C. G. Callan, L. Thorlacius, Nucl. Phys. B, 329 (1990), 117 ; C. G. Callan, A. G. Felce, D. E. Freed, Nucl. Phys., 392 (1993), 551 | DOI | MR | DOI | MR

[6] M. D. Kostin, J. Chem. Phys., 57 (1972), 3589 | DOI

[7] H. Dekker, Z. Phys. B, 21 (1975), 295 ; Phys. Rev. A, 16 (1977), 2116 | DOI | DOI | MR

[8] S. Nakamiya, Prog. Theor. Phys., 20 (1958), 948 ; I. R. Senitzky, Phys. Rev., 150 (1960), 670 ; R. Zwanzig, J. Chem. Phys., 33 (1960), 1338 ; H. Mori, Prog. Theor. Phys., 33 (1965), 423 | DOI | MR | DOI | MR | DOI | MR | DOI | Zbl

[9] A. O. Caldeira, A. J. Legget, Physica A, 121 (1983), 587 ; Phys. Rev. Lett., 46 (1981), 211 ; Ann. Phys., 149 (1983), 374 | DOI | MR | Zbl | DOI | MR | DOI

[10] A. P. Polychronakos, R. Tzani, Phys. Lett. B, 302 (1993), 255 | DOI | MR

[11] C. G. Callan(jr.), D. Freed, Nucl. Phys., 374 (1992), 543 | DOI | MR | Zbl

[12] K. Yasue, Ann. Phys., 114 (1978), 479 | DOI

[13] E. Nelson, Phys. Rev., 150 (1966), 1079 | DOI

[14] G. Parisi, Y. S. Wu, Sci. Sin., 24 (1981), 483 | MR

[15] J. R. Klauder, Act. Phys. Austr. Suppl., 25 (1983), 251 ; H. Gausterer, J. R. Klauder, Phys. Rev., 33 (1986), 251 ; J. Ambjorn, M. Flensburg, C. Peterson, Nucl. Phys., 275 (1986), 375 ; J. Ambjorn, S. K. Yang, Nucl. Phys., 275 (1986), 18 ; J. Ambjorn, Proceedings, Quarks'86 (Tbilisi, 1986), 303–315; A. P. Polychronakos, R. Tzani, Phys. Lett. B, 259 (1991), 291 | MR | DOI | MR | DOI | MR | DOI | DOI | MR