Voir la notice de l'article provenant de la source Math-Net.Ru
@article{FAA_1972_6_4_a4, author = {A. M. Perelomov}, title = {Coherent states and theta functions}, journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a}, pages = {47--57}, publisher = {mathdoc}, volume = {6}, number = {4}, year = {1972}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/FAA_1972_6_4_a4/} }
A. M. Perelomov. Coherent states and theta functions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 6 (1972) no. 4, pp. 47-57. http://geodesic.mathdoc.fr/item/FAA_1972_6_4_a4/
[1] Fon Neiman I., Matematicheskie osnovy kvantovoi mekhaniki, Nauka, M., 1964 | MR
[2] Glauber R.J., “The quantum theory of optical coherence”, Phys. Rev., 130 (1963), 2529–2539 | DOI | MR
[3] Klauder Dzh., Sudarshan E., Osnovy kvantovoi optiki, Mir, M., 1970
[4] Zeldovich B.Ya., Perelomov A.M., Popov B.C., “Relaksatsiya kvantovogo ostsillyatora”, ZhETF, 55 (1968), 589–606; “Релаксация квантового осциллятора при наличии внешней силы”, ЖЭТФ, 57 (1969), 196–206; Релаксация квантового осциллятора. I, II, препринты No 612, 618, ИТЭФ, 1968
[5] Perelomov A.M., “Zamechanie o polnote sistemy kogerentnykh sostoyanii”, TMF, 6 (1971), 213–224 | MR
[6] Cartier P., “Quantum mechanical commutation relations and theta-functions”, Proc. Symp. Pure Math., 9 ; Algebraic groups and discontinuous subgroups, Providence, 1966, 361–383 | MR | DOI | Zbl
[7] Weyl H., Gruppentheorie und Quantenmechanik, Leipzig, 1928 | MR
[8] Krazer A., Lehrbuch der Thetafunktionen, Leipzig, 1903 | MR | Zbl
[9] Coble A.B., Algebraic geometry and theta-functions, Amer. Math. Soc. Coll. Publ., X, N. Y., 1929 | MR
[10] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, v. 3, Nauka, M., 1967 | MR
[11] Weil A., “Sur certains groupes d'operateurs unitaires”, Acta Math., 111 (1964), 143–211 ; Matematika, 13:5 (1969), 33–94 | DOI | MR | Zbl
[12] Fock V.A., “Verallgemeinerung und Losung der Diracschen Statistischen Gleichung”, Z. Phys., 49 (1928), 339–357 | DOI | Zbl
[13] Segal I.E., Mathematical problems of relativistic physics, Rhode Island, 1963 | MR
[14] Vargmann V., “On a Hilbert space of analytic functions. I”, Comm. Pure Appl. Math., 14 (1961), 187–214 | DOI | MR
[15] Pepelomov A.M., “Coherent states for arbitrary Lie group”, Comm. Math. Phys., 26 (1972), 222–236 | DOI | MR
[16] Gelfand I.M., Graev M.I., Pyatetskii-Shapiro I.I., Teoriya predstavlenii i avtomorfnye funktsii, Nauka, M., 1966 | MR
[17] Zigel K.L., Avtomorfnye funktsii neskolkikh kompleksnykh peremennykh, IL, M., 1954
[18] Chzhen Shen-shen, Kompleksnye mnogoobraziya, IL, M., 1961
[19] Igusa J., “On the graded ring of theta-constants. I, II”, Amer. J. Math., 86 (1964), 219–246 ; 88 (1966), 221–236 | DOI | MR | Zbl | DOI | MR | Zbl