The Two-Dimensional Symplectic and Metaplectic Groups and Their Universal Cover

作者: R. Simon , N. Mukunda

DOI: 10.1007/978-1-4899-1219-0_55

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摘要: We give a detailed discussion of the group Sp(2, R), organized in such way as to lead explicit constructive descriptions metaplectic Mp(2) and universal covering \( {S_p}\left( {2,R} \right) \) . The aim is make clear easily visible fashion global topological relationships among these groups physical relevance, practical calculations with them feasible. properties one parameter subgroups exponential map, Iwasawa decomposition, are also investigated detail for groups.

参考文章(21)
L.C. Biedenharn, UNITARY REPRESENTATIONS OF THE NON-COMPACT FAMILY OF GROUPS SU(p,1). pp 23-41 of Non-Compact Groups in Particle Physics. Chow, Yutze (ed.). New York, W. A. Benjamin, Inc., 1966.. ,(1967)
Lawrence Biedenharn, Angular momentum in quantum physics ,(1981)
E. C. G Sudarshan, N. Mukunda, Classical Dynamics: A Modern Perspective ,(1974)
Shlomo Sternberg, Victor Guillemin, Symplectic Techniques in Physics ,(1984)
I. Ferretti, M. Verde, On the wigner coefficients of the three-dimensional Lorentz group Nuovo Cimento Della Societa Italiana Di Fisica A-nuclei Particles and Fields. ,vol. 55, pp. 110- 124 ,(1968) , 10.1007/BF02760110
R. Simon, N. Mukunda, E. C. G. Sudarshan, Hamilton's theory of turns generalized to Sp(2,R). Physical Review Letters. ,vol. 62, pp. 1331- 1334 ,(1989) , 10.1103/PHYSREVLETT.62.1331
André Weil, Sur certains groupes d'opérateurs unitaires Acta Mathematica. ,vol. 111, pp. 143- 211 ,(1964) , 10.1007/BF02391012
Kuo‐Hsiang Wang, Clebsch‐Gordan Series and the Clebsch‐Gordan Coefficients of O(2, 1) and SU(1, 1) Journal of Mathematical Physics. ,vol. 11, pp. 2077- 2095 ,(1970) , 10.1063/1.1665368