Geodesic
Methods of Weyl representation of the phase space and canonical transformations. I
Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 3, pp. 347-363 Cet article a éte moissonné depuis la source Math-Net.Ru

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The structure of the kernel of a canonical transformation and a differential equation for the symbol of the intertwining operator are found. The symbol of a general linear canonical transformation is constructed in terms of a Cayley transformation of the symplectic transformation of the phase space. Its singularities and applications to group theory are studied. The Green's functions and spectral projectors of arbitrary quadratic systems are constructed using the classification methods of classical mechanics. 
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     author = {V. G. Budanov},
     title = {Methods of {Weyl} representation of the phase space and canonical {transformations.~I}},
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     pages = {347--363},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1984_61_3_a2/}
}
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V. G. Budanov. Methods of Weyl representation of the phase space and canonical transformations. I. Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 3, pp. 347-363. http://geodesic.mathdoc.fr/item/TMF_1984_61_3_a2/

[1] Weyl H., Gruppentheoric und Quantenmechanik, Hizzel-Verlag, Leipzig, 1928 | MR

[2] Wigner E. P., Phys. Rev., 40 (1932), 749–768 | DOI

[3] Moyal J. E., Proc. Cambr. Phil. Soc., 45 (1949), 99–118 ; Мойэл Д. Э., Вопросы причинности в квантовой механике, ИЛ, М., 1955 | DOI | MR

[4] Shirokov Yu. M., TMF, 25:3 (1975), 307–312 ; 28:3 (1976), 308–319 ; ЭЧАЯ, 10:1 (1979), 5–50 | MR | Zbl | MR | Zbl | MR

[5] Berezin F. A., UFN, 132:3 (1980), 497–589 ; Березин Ф. А., Шубин М. А., Уравнение Шредингера, МГУ, М., 1983 | DOI | MR | MR

[6] Marinov M. S., Phys. Rep. C, 60:1 (1980), 1–57 | DOI | MR

[7] Polubarinov I. V., Teoretiko-gruppovye metody v fizike, T. II, Nauka, M., 1983, 189–200

[8] Faddeev L. D., Yakubovskii O. A., Lektsii po kvantovoi mekhanike, dlya studentov - matematikov, LGU, L., 1980 | MR

[9] Remler E. A., Ann. of Phys., 95 (1975), 455–495 | DOI | MR

[10] Berezin F. A., Marinov M. S., Ann. Phys., 104 (1977), 336–362 | DOI | Zbl

[11] Tatarskii V. I., UFN, 139:4 (1983), 587–620 | DOI | MR

[12] De Groot S. R., Sattorp L. G., Elektrodinamika, Nauka, M., 1982

[13] Antonets M. A., Matem. sb., 107:1 (1978), 20–36 ; ТМФ, 38:3 (1979), 331–344 | MR | Zbl | MR

[14] Daubechies I., Arossmann A., Reigner J., J. Math. Phys., 24 (1983), 239–255 | DOI | MR

[15] Leaf B., J. Math. Phys., 9 (1968), 65–72 | DOI | Zbl

[16] Balazs N. L., Jennings B. K., Phys. Rep. C, 104:6 (1984), 5–36 | DOI | MR

[17] Gerasimeno V. I., TMF, 50:1 (1982), 77–87 | MR

[18] Bayen F., Flato M., Froundal C., Lichnerowicz A., Sterheimer D., Ann. of Phys., 111 (1978), 61–110 ; 111–135 | DOI | MR | Zbl | MR

[19] Buslaev V. S., Skriganov M. M., TMF, 2:3 (1970), 292–296 | MR

[20] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 | MR

[21] Agarwal G. S., Wolf E., Phys. Rev. D, 2 (1970), 2161–2186 ; 2187–2205 | DOI | MR | Zbl | Zbl

[22] Berezin F. A., Metod vtorichnogo kvantovaniya, Nauka, M., 1965 | MR

[23] Malkin I. A., Manko V. I., Dinamicheskie simmetrii i kogerentnye sostoyaniya kvantovykh sistem, Nauka, M., 1979 | MR

[24] Manko V. I., Trifonov D. A., Teoretiko-gruppovye metody v fizike, T. II, Nauka, M., 1983, 46–56 | MR

[25] Groenewold H. J., Physica, 12 (1946), 405–417 | DOI | MR

[26] Mello P. A., Mochinsky M., J. Math. Phys., 16 (1975), 2017–2028 | DOI | MR

[27] Riss F., Sekefalvi-Nad B., Lektsii po funktsionalnomu analizu, Mir, M., 1979 | MR

[28] Baz A. I., Zeldovich Ya. B., Perelomov A. M., Rasseyanie, reaktsii i raspady v nerelyativistskoi kvantovoi mekhanike, Nauka, M., 1971 | Zbl

[29] Perelomov A. M., UFN, 123:1 (1977), 23–56 | DOI

[30] Barut A., Ronchka R., Teoriya predstavlenii grupp i ee prilozheniya, Mir, M., 1980 | MR | Zbl

[31] Gilmor R., Prikladnaya teoriya katastrof, Mir, M., 1984 | MR | Zbl