Bosonic and fermionic white noises and the reflection process
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 1, pp. 36-47 Cet article a éte moissonné depuis la source Math-Net.Ru

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The reflection process is used to unify the bosonic and fermionic quantum stochastic calculi. But the reflection process cannot be converted to the standard Stratonovich form. It is shown that an analytically extended version of the Stratonovich calculus allows describing the reflection process at the bosonic white-noise level as well as constructing the fermionic white-noise variables.
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J. Gough. Bosonic and fermionic white noises and the reflection process. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 1, pp. 36-47. http://geodesic.mathdoc.fr/item/TMF_2000_124_1_a2/

[1] R. L. Hudson, K. R. Parthasarathy, Commun. Math. Phys., 93 (1984), 301–323 | DOI | MR | Zbl

[2] G. Lindblad, Commun. Math. Phys., 48 (1976), 19–30 | DOI | MR

[3] Dzh. Gokh, TMF, 111:2 (1997), 218–233 | DOI | MR

[4] Dzh. Gokh, TMF, 113:2 (1997), 276–284 | DOI | MR

[5] J. Gough, “Asymptotic Stochastic Transformations for Non-Linear Quantum Dynamical Systems”, Rep. Math. Phys. (to appear) | MR

[6] L. Accardi, J. Gough, Y. G. Lu, Rep. Math. Phys., 36:2/3 (1995), 155–187 | DOI | MR | Zbl

[7] R. L. Hudson, K. R. Parthasarathy, Commun. Math. Phys., 104 (1986), 457–470 | DOI | MR | Zbl

[8] J. Dieudonné, Foundations of Modern Analysis, Academic Press International Edition, New York, 1968 | MR

[9] C. W. Gardiner, Quantum Noise, Springer-Verlag, New York, 1991 | MR | Zbl

[10] T. M. W. Eyre, Quantum Stochastic Calculus and Representations of Lie Super Algebras, Lecture Notes in Mathematics, 1692, Springer, Berlin, 1998 | DOI | MR

[11] D. Applebaum, Commun. Math. Phys., 96 (1984), 473–496 | DOI | MR | Zbl

[12] L. Accardi, Y. G. Lu, A. Frigerio, R. Alicki, “An invitation to the weak coupling and low density limit”, Quantum Probability and Related Topics, VI, ed. L. Accardi, World Scientific, Singapore, 1991, 3–31 | DOI | MR

[13] L. Accardi, A. Frigerio, Y. G. Lu, Acta Appl. Math., 26 (1992), 197–208 | DOI | MR | Zbl

[14] J. Gough, “Asymptotic Stochastic Transformations for Non-linear Quantum Dynamical Systems”, Rep. Math. Phys. (to appear) | MR

[15] J. Gough, Potential Anal., 11:3 (1999), 213–233 | DOI | MR | Zbl

[16] R. L. Hudson, R. F. Streater, Phys. Lett. A, 86 (1981), 277 | DOI | MR

[17] W. von Waldenfels, “Ito Solution of the Linear Quantum Stochastic Differential Equation describing Light Emission and Absorption”, Quantum Probability and Aplications to the Quantum Theory of Irreversible Processes, Proc. Int. Workshop (Villa Mondragone, Italy, Sept. 6–11, 1982), Lect. Notes in Math., 1055, eds. L. Accardi, A. Frigerio, V. Gorini, Springer, Berlin, 1984, 384–411 | DOI | MR

[18] A. M. Chebotarev, Matem. zametki, 61:4 (1997), 612–622 | DOI | MR | Zbl