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Ali, S. Twareque; Prugovečki, Eduard

Harmonic analysis and systems of covariance for phase space representation of the Poincaré group. (English) Zbl 0603.22012

Acta Appl. Math. 6, 47-62 (1986).
The spin zero phase space representation of the Poincaré group is studied following the corresponding investigation for the Galilei group carried out by the authors in a previous paper [Acta Appl. Math. 6, 19-45 (1986; see the preceding review)]. Again, the spaces of the irreducible subrepresentations are reproducing kernel Hilbert spaces; the related systems of covariance are analyzed.
Reviewer: U.Cattaneo

Cited in 2 Reviews
Cited in 9 Documents

MSC:

22E70 Applications of Lie groups to the sciences; explicit representations
81T60 Supersymmetric field theories in quantum mechanics
83A05 Special relativity
81T20 Quantum field theory on curved space or space-time backgrounds

Keywords:

POV measures; harmonic analysis; relativistic phase space representation; Poincaré group; reproducing kernel Hilbert spaces; systems of covariance

Citations:

Zbl 0603.22011; Zbl 0603.22010
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Full Text: DOI

References:

[1] Ali, S. T. and Prugovečki, E.: Acta Appl. Math. 6 (1986), 19–45. · Zbl 0603.22011 · doi:10.1007/BF00046933
[2] Prugovečki, E.: Stochastic Quantum Mechanics and Quantum Spacetime, D. Reidel, Dordrecht, 1984.
[3] Hegerfeldt, G. C.: Phys. Rev. D10 (1974), 3320.
[4] Skagerstam, B. K.: Int. J. Theor. Phys. 15 (1976), 213. · doi:10.1007/BF01807094
[5] Hegerfeldt, G. C. and Ruijsenaars, S. N. M.: Phys. Rev. 22 (1980), 377.
[6] Wigner, E. P.: Ann. Math. 40 (1939), 149. · Zbl 0020.29601 · doi:10.2307/1968551
[7] Barut, A. O. and R\(\backslash\)caczka, R.: Theory of Group Representations and Applications, PWN, Warsaw, 1977.
[8] Bogolubov, N. N., Logunov, A. A., and Todorov, I. T.: Introduction to Axiomatic Quantum Field Theory, Benjamin, Reading, Mass. (1975).
[9] Prugovečki, E.: Quantum Mechanics in Hilbert Space, 2nd edn, Academic Press, New York and London, 1981.
[10] Blokhintsev, D. I.: Space and Time in the Microworld, D. Reidel, Dordrecht, 1973. · Zbl 0254.53009
[11] Prugovečki, E.: J. Math. Phys. 19 (1978), 2260. · doi:10.1063/1.523602
[12] Prugovečki, E.: Phys. Rev. D18 (1978), 3655.
[13] Prugovečki, E.: Rep. Math. Phys. 17 (1980), 401. · doi:10.1016/0034-4877(80)90007-5
[14] Ehlers, J.: in B. K.Sachs (ed.), General Relativity and Cosmology, Academic Press, New York and London, 1971.
[15] Ali, S. T.: J. Math. Phys. 20 (1979), 1385. · Zbl 0452.22023 · doi:10.1063/1.524245
[16] Ali, S. T.: J. Math. Phys. 21 (1980), 818. · Zbl 0487.22016 · doi:10.1063/1.524461
[17] Hewitt, E. and Ross, K. A.: Abstract Harmonic Analysis, vol. II., Springer, Berlin, 1970. · Zbl 0213.40103
[18] Cattaneo, U.: J. Math. Phys. 23 (1982), 659. · doi:10.1063/1.525413
[19] Newton, T. D. and Wigner, E. P.: Rev. Mod. Phys. 21 (1949), 400. · Zbl 0036.26704 · doi:10.1103/RevModPhys.21.400
[20] Wightman, A. S.: Rev. Mod. Phys. 34 (1962), 845. · doi:10.1103/RevModPhys.34.845
[21] Ali, S. T.: ’Harmonic Analysis of Phase Space I: Reproducing Kernel Hilbert Spaces, POV Measures and Systems of Covariance’, (to appear).
[22] Riesz, F. and Sz-Nagy, B.: Functional Analysis: Appendix, Frederick Ungar, New York, 1960.
[23] Ali, S. T. and Prugovečki, E.: Nuovo Cim. A 63 (1981), 171. · doi:10.1007/BF02902668
[24] Prugovečki, E.: Nuovo Cim. A 89 (1985), 105. · doi:10.1007/BF02804854
[25] Prugovečki, E.: ’General Relativistic and Gauge Invariant Quantum Geometries’, University of Toronto preprint.
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