Geodesic
Nonstationary generalized Duru–Kleinert transformation of path integrals for systems of differential equations in the one-dimensional space
Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 1, pp. 17-27 
S. N. Storchak. Nonstationary generalized Duru–Kleinert transformation of path integrals for systems of differential equations in the one-dimensional space. Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 1, pp. 17-27. http://geodesic.mathdoc.fr/item/TMF_1996_109_1_a1/
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     author = {S. N. Storchak},
     title = {Nonstationary generalized {Duru{\textendash}Kleinert} transformation of path integrals for systems of differential equations in the one-dimensional space},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {17--27},
     year = {1996},
     volume = {109},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_109_1_a1/}
}
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New formulas for transformations of the Winer continual integrals corresponding to parabolic systems of differential equations in the one-dimensional space are obtained. Namely, we consider the systems of two equations with time-dependent coefficients. These formulas determine the continual integral transformation under the reonomic homogeneous point-like transformation of the integration variables together with the path reparametrization transformation. These formulas result in the integral relation between Green functions of the related systems of differential equations. It is shown how the generalized Schepp formula for the continual integrals under consideration arises from this relation. In order to derive these new formulas, the properties of random processes under the phase transitions and the random change of time were used.

[1] I. H. Duru, H. Kleinert, Phys. Lett., 84B (1979), 185 | DOI | MR

[2] N. K. Pak, I. Sokmen, Phys. Rev., A30 (1984), 1629 ; F. Steiner, Phys. Lett., 106A (1984), 356 ; C. DeWitt-Morette, A. Young, Ann. Phys., 169 (1986), 140 ; C. Grosche, F. Steiner, Z. Phys., C36 (1987), 699 ; S. N. Storchak, Path reparametrization in the path integral for Morse potential, IHEP Preprint 82–20, Serpukhov, 1982; IHEP Preprint 86–143, Serpukhov, 1986; С. Н. Сторчак, ТМФ, 75 (1988), 403 ; 93 (1992), 17 ; 94 (1993), 375 ; 101 (1994), 374 | DOI | MR | DOI | MR | DOI | MR | Zbl | MR | MR | MR | Zbl | MR | Zbl | MR | Zbl

[3] S. N. Storchak, Phys. Lett., A135 (1989), 77 | DOI | MR

[4] S. N. Storchak, Phys. Lett., A161 (1992), 397 | DOI | MR

[5] C. Grosche, Phys. Lett., A182 (1993), 28 | DOI | MR

[6] A. Pelster, A. Wunderlin, Z. Phys., B89 (1992), 373 | DOI

[7] S. N. Storchak, Path reparametrization in the path integrals for the systems of differential equation in one-dimensional space, IHEP Preprint 92–133, Serpukhov, 1992 | MR | Zbl

[8] Ph. Blanchard, M. Sirugue, J. Math. Phys., 22 (1981), 1372 | DOI | MR | Zbl

[9] L. A. Shepp, Ann. Math. Stat., 37 (1966), 321 | DOI | MR | Zbl

[10] E. Onofri, Lett. Nuovo Cim., 21 (1978), 489 | DOI

[11] Yu. L. Daletskii, N. I. Teterina, UMN, 27:2 (1972), 167 ; Я. И. Белопольская, Ю. Л. Далецкий, УМН, 37:3 (1982), 95 ; Ю. Л. Далецкий, УМН, 38:3 (1983), 87 | MR | MR | Zbl | MR