Simon, Barry The classical limit of quantum partition functions. (English) Zbl 0436.22012 Commun. Math. Phys. 71, 247-276 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 75 Documents MSC: 22E70 Applications of Lie groups to the sciences; explicit representations 22C05 Compact groups 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations 81T08 Constructive quantum field theory Keywords:quantum partition functions; coherent vectors; classical limit; microstable potentials; compact Lie group × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Adams, J.F.: Lectures on Lie groups. New York: Benjamin 1969 · Zbl 0206.31604 [2] Asano, T.: Prog. Theo. Phys.40, 1328 (1968); J. Phys. Soc. Japan25, 1220 (1968) · doi:10.1143/PTP.40.1328 [3] Berezin, F.: Math. USSR 5688, 269 (1972) · Zbl 0279.47006 · doi:10.1070/SM1972v017n02ABEH001504 [4] Berezin, F.: Math. USSR Izv.6, 117 (1972) · Zbl 0259.47004 · doi:10.1070/IM1972v006n05ABEH001913 [5] Berezin, F.: Commun. Math. Phys.40, 153 (1975) · Zbl 1272.53082 · doi:10.1007/BF01609397 [6] Boerner, H.: Representations of groups. Amsterdam: North Holland 1970 [7] Combes, J., Schrader, R., Seiler, R.: Ann. Phys.111, 1 (1978) · doi:10.1016/0003-4916(78)90221-X [8] Dunlop, F., Newman, C.: Commun. math. Phys.44, 223 (1975) · doi:10.1007/BF01609827 [9] Fuller, W., Lenard, A.: Commun. math. Phys.69, 99 (1979) · doi:10.1007/BF01941327 [10] Gilmore, R.: Ann. Phys.74, 391 (1972) · doi:10.1016/0003-4916(72)90147-9 [11] Gilmore, R.: Rev. Mex. de Fis.23, 143 (1974) [12] Gilmore, R.: J. Math. Phys.20, 891 (1979) · doi:10.1063/1.524137 [13] Golden, S.: Phys. Rev.137, 1127 (1965) · doi:10.1103/PhysRev.137.B1127 [14] Griffiths, R.: J. Math. Phys.10, 1559 (1969) · doi:10.1063/1.1665005 [15] Hepp, K., Lieb, E.: Phys. Rev.8A, 2517 (1973) [16] Hess, H., Schrader, R., Uhlenbrock, D.: Duke Math. J.44, 893 (1977) · Zbl 0379.47028 · doi:10.1215/S0012-7094-77-04443-X [17] Kato, T.: In: Topics in analysis, pp. 185-195. London, New York: Academic Press 1978 [18] Klauder, J.: Ann. Phys.11, 123 (1960) · Zbl 0098.20804 · doi:10.1016/0003-4916(60)90131-7 [19] Klauder, J.: J. Math. Phys.5, 177 (1964) · Zbl 0137.23901 · doi:10.1063/1.1704107 [20] Kostant, B.: Lecture notes in mathematics170, p. 87. Berlin, Heidelberg, New York: Springer 1970 · Zbl 0223.53028 · doi:10.1007/BFb0079068 [21] Kostant, B.: Private communication [22] Levin, S.: Private communication [23] Lieb, E.: Commun. math. Phys.31, 327 (1973) · Zbl 1125.82305 · doi:10.1007/BF01646493 [24] Lieb, E., Simon, B.: Adv. Math.23, 22-116 (1977) · Zbl 0938.81568 · doi:10.1016/0001-8708(77)90108-6 [25] Parthasarathy, K., Ranga Rao, R., Varadarajan, V.S.: Ann. Math.85, 383 (1967) · Zbl 0177.18004 · doi:10.2307/1970351 [26] Perelomov, S.: Commun. math. Phys.26, 222 (1972) · Zbl 0243.22016 · doi:10.1007/BF01645091 [27] Reed, M., Simon, B.: Methods of modern mathematical physics, IV. Analysis of operators. New York, London: Academic Press 1978 · Zbl 0401.47001 [28] Robinson, D.:The thermodynamic pressure in quantum statistical mechanics. Berlin, Heidelberg, New York: Springer 1971 [29] Ruelle, D.: Statistical mechanics. New York: Benjamin 1969 · Zbl 0177.57301 [30] Samelson, H.: Notes on Lie algebras. Wokingham: van Nostrand 1969 · Zbl 0209.06601 [31] Simon, B.: Ind. Math. J.26, 1067 (1977) · Zbl 0389.47021 · doi:10.1512/iumj.1977.26.26086 [32] Simon, B.: J. Func. Anal.32, 97 (1979) · Zbl 0413.47037 · doi:10.1016/0022-1236(79)90079-X [33] Simon, B.: J. Op. Theory,1, 37 (1979) [34] Simon, B.: Adv. Math.30, 268 (1978) · Zbl 0414.35069 · doi:10.1016/0001-8708(78)90040-3 [35] Simon, B.: Trace ideal and their applications. Cambridge: Cambridge University Press, 1979 · Zbl 0423.47001 [36] Simon, B.: Functional integration and quantum physics. New York, London: Academic Press 1979 · Zbl 0434.28013 [37] Simon, B.: In: Proc. 1979 Random Fields Colloq., Hungary [38] Souriau, J.: Structures des systèmes dynamiques. Paris: Dunod 1972 [39] Suzuki, M., Fisher, M.: J. Math. Phys.12, 235 (1971) · doi:10.1063/1.1665583 [40] Thirring, W.: Lectures on physics, Vol. 4; Univ. of Vienna Mimeographed notes; German publication expected 1980; English translation, 1981 [41] Thompson, C.: J. Math. Phys.6, 1812 (1965); Ind. Math. J.21, 469 (1971) · doi:10.1063/1.1704727 [42] Wehrl, A.: Rep. Math. Phys.12, 385 (1977) · Zbl 0379.60098 · doi:10.1016/0034-4877(77)90034-9 [43] Baumgartner, B.: Commun. Math. Phys. to appear This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.