A representation independent propagator. II : Lie groups with square integrable representations
Annales de l'I.H.P. Physique théorique (1996)
- Volume: 65, Issue: 2, page 175-222
- ISSN: 0246-0211
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topTomé, Wolfgang. "A representation independent propagator. II : Lie groups with square integrable representations." Annales de l'I.H.P. Physique théorique 65.2 (1996): 175-222. <http://eudml.org/doc/76740>.
@article{Tomé1996,
author = {Tomé, Wolfgang},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {representation independent propagator; real, compact Lie group; square integrable representations; curved manifold},
language = {eng},
number = {2},
pages = {175-222},
publisher = {Gauthier-Villars},
title = {A representation independent propagator. II : Lie groups with square integrable representations},
url = {http://eudml.org/doc/76740},
volume = {65},
year = {1996},
}
TY - JOUR
AU - Tomé, Wolfgang
TI - A representation independent propagator. II : Lie groups with square integrable representations
JO - Annales de l'I.H.P. Physique théorique
PY - 1996
PB - Gauthier-Villars
VL - 65
IS - 2
SP - 175
EP - 222
LA - eng
KW - representation independent propagator; real, compact Lie group; square integrable representations; curved manifold
UR - http://eudml.org/doc/76740
ER -
References
top- [1] E.W. Aslaksen and J.R. Klauder, Unitary representations of the affine group, J. Math. Phys., Vol. 9, 1968, pp. 206-211. Zbl0162.58403MR233925
- [2] E.W. Aslaksen and J.R. Klauder, Continuous representation theory using the affine group, J. Math. Phys., Vol. 10, 1969, pp. 2267-2275. Zbl0184.54601MR256642
- [3] A.O. Barut and R. Rączka, "Theory of Group Representations and Applications," second revised edition, World Scientific, Singapore, 1986. Zbl0644.22011MR889252
- [4] A. Böhm, "The Rigged Hilbert Space and Quantum Mechanics", Springer Verlag, Berlin1978. Zbl0388.46045MR503149
- [5] F. Bruhat, Distributions sur un groupe localement compact et applications à l'étude des représentations des groupes p-adiques, Bull. Soc. Math. France, Vol. 89, 1961, pp. 43-75. Zbl0128.35701MR140941
- [6] A.L. Carey, Square-integrable representations of non-unimodular groups, Bull. Austral. Math. Soc., Vol. 15, 1976, pp. 1-12. Zbl0327.22008MR430146
- [7] J. Dixmier, "C*-Algebras", North Holland, Amsterdam, 1977. Zbl0372.46058MR458185
- [8] M. Duflo and C.C. Moore, On the regular representation of a nonunimodular locally compact group, J. Funct. Anal., Vol. 21, 1976, pp. 209-243. Zbl0317.43013MR393335
- [9] N. Dunford and J. Schwartz, "Linear Operators", Part 1, Wiley, New York, 1958. Zbl0084.10402
- [10] M. Flato, J. Simon, H. Snellman and D. Sternheimer, Simple facts about analytic vectors and integrability, Ann. scient. Éc. Norm. Sup., Vol. 5, 1972, pp. 423-434. Zbl0239.22019MR376960
- [11] I.M. Gel'fand and M.A. Neumark, Unitary representations of the group of linear transformations of the straight line [russ.], DokladyAkad. Nauk SSSR, Vol. 55, 1947, pp. 571-574. Zbl0029.00503MR20559
- [12] R. Haag, "Local Quantum Physics: Fields, Particles, Algebras", Springer Verlag, Berlin, 1992. Zbl0777.46037MR1182152
- [13] C.J. Isham and J.R. Klauder, Coherent states for n-dimensional Euclidean groups E(n) and their application, J. Math. Phys., Vol. 32, 1991, pp. 607-620. Zbl0735.22012MR1093798
- [14] J.R. Klauder, Path integrals, Acta Phys. Austriaca Suppl., Vol. XXII, 1980, pp. 3-49. MR602334
- [15] J.R. Klauder, "Path Integrals for Affine Variables." In: J. P. Antoine and E. Tirapequi (eds.), Functional Integration Theory and Applications, Proceedings, pp. 101-119, Plenum, New York, 1980. Zbl0481.28012MR602176
- [16] J.R. Klauder, "The universal propagator." In: D. Han, Y. S. Kim and W. W. Zachary (eds.), Workshop on Harmonic Oscillators, Proceedings, Maryland, USA, 1992, pp. 19- 28, NASA Publication 3197, 1993.
- [17] J.R. Klauder and B.-S. Skagerstam, "Coherent States: Applications in Physics and Mathematical Physics", World Scientific, Singapore, 1985. Zbl1050.81558MR826247
- [18] J.R. Klauder and W.A. Tomé, The universal propagator for affine [or SU(1,1)] coherent states, J. Math. Phys., Vol. 33, 1992, pp. 3700-3709. Zbl0780.46039MR1185844
- [19] K. Maurin, "General Eigenfunction Expansions and Unitary Representations of Topological Groups", PWN-Polish Scientific Publishers, Warsaw, 1968. Zbl0185.39001MR247377
- [20] H. Meschkowski, "Hilbertsche Raume mit Kernfunktion", Springer Verlag, Berlin, 1962. Zbl0103.08802MR140912
- [21] E. Nelson, Analytic vectors, Ann. of Math., Vol. 70, 1959, pp. 572-615. Zbl0091.10704MR107176
- [22] L.S. Schulman, "Techniques and Applications of Path Integration", Wiley, New York, 1981. Zbl0587.28010MR601595
- [23] W.A. Tomé, A representation independent propagator. I. Compact Lie groups, Ann. Inst. Henri Poincaré, Theor. Phys., Vol. 63, 1995, pp. 1-40. Zbl0842.22025MR1354438
- [24] T.T. Troung, New integral equations for the quartic anharmonic oscillator, Nuovo Cimento Lett., Vol. 9, 1974, pp. 533-536.
- [25] T.T. Troung, Weyl quantization of anharmonic oscillators, J. Math. Phys., Vol. 16, 1975, pp. 1034-1043. MR375996
- [26] G. Tulsian and J.R. Klauder, The universal propagator for E(2) coherent states, Commun. Theor. Phys., Vol. 5 (to appear). MR1369180
- [27] L.G. Yaffe, Large N limits as classical mechanics, Rev. Mod. Phys., Vol. 54, 1982, pp. 407-435. MR694200
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