Realizations of Representations of the Poincaré Group and Associated Similarity Transformations

J. Beckers

doi:10.1103/PhysRevD.3.952

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Realizations of Representations of the Poincaré Group and Associated Similarity Transformations

J. Beckers

Service de Physique Mathématique, Université de Liège, Liège, Belgium

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Phys. Rev. D 3, 952 – Published 15 February, 1971

DOI: https://doi.org/10.1103/PhysRevD.3.952

Abstract

Recent contributions on canonical and manifestly covariant realizations of the representations of the Poincaré group are discussed. A $2 (2 j + 1)$ -dimensional operator for arbitrary spin $j$ is constructed, permitting simple interpretations and discussions of similarity transformations currently used in the literature.

References (35)

G. Parravicini, A. Sparzani, and M. Pauri, Nuovo Cimento Letters 1, 295 (1969)
G. Parravicini and A. Sparzani, University of Milan Report No. FUM 0/103/FT, 1969 (unpublished)
I. M. Gel'fand, R. A. Minlos, and Z. Ya. Shapiro, Representations of the Rotation and Lorentz Groups and Their Applications (Oxford U. P., London, 1963)
L. L. Foldy, Phys. Rev. 102, 568 (1956)
L. L. Foldy and S. A. Wouthuysen, Phys. Rev. 78, 29 (1950)
E. P. Wigner, Ann. Math. 40, 149 (1939)
V. Bargmann and E. P. Wigner, Proc. Natl. Acad. Sci. U. S. 34, 211 (1948)
Yu. M. Shirokov, Zh. Eksperim. i Teor. Fiz. 33, 861 (1957) ibid.33, 1196 (1957) ibid.33, 1208 (1957) Soviet Phys. JETP 6, 664 (1958) Soviet Phys. JETP6, 919 (1958) Soviet Phys. JETP6, 929 (1958)
A. S. Wightman, in Dispersion Relations and Elementary Particles, Les Houches (Hermann, Paris, 1960), p. 159
H. Joos, Fortschr. Physik 10, 65 (1962)
R. Shaw, Nuovo Cimento 33, 1074 (1964)
S. Weinberg, Phys. Rev. 133, B1318 (1964)
P. Moussa and R. Stora, in Boulder Lectures in Theoretical Physics, edited by W. E. Brittin and A. O. Barut (Colorado U. P., Boulder, 1965), Vol. VIIA, p. 37
([15]) and ([16])
P. Winternitz, Rutherford Laboratory Report No. RPP/T/3, 1969 (unpublished)
A. P. Balachandran, Syracuse University Report No. NYO-3399-272, SU-7206-272, 1969 (unpublished)
C. Fronsdal, Phys. Rev. 113, 1367 (1959)
D. L. Weaver, C. L. Hammer, and R. H. Good, Jr., Phys. Rev. 135, B241 (1964)
D. L. Pürsey, Ann. Phys. (N.Y.) 32, 157 (1965)
W. K. Tung, Phys. Rev. 156, 1385 (1967)
Omitted endnote
A. Chakrabarti, J. Math. Phys. 4, 1215 (1963)
J. Sesma, J. Math. Phys. 7, 1300 (1966)
J. A. De Azcarraga and L. J. Boya, J. Math. Phys. 9, 1689 (1968)
J. A. De Azcarraga and L. Oliver, J. Math. Phys. 10, 1869 (1969)
[11]
Sec. III of [19]
[22]
([22–24,30])
A. Chakrabarti, J. Math. Phys. 4, 1223 (1963)
A. Chakrabarti, J. Math. Phys. 7, 949 (1966)
J. J. Giambiagi, Nuovo Cimento 16, 202 (1960)
C. G. Bollini and J. J. Giambiagi, Nuovo Cimento 21, 107 (1961)
R. H. Good, Jr. and M. E. Rose, Nuovo Cimento 24, 864 (1962)
H. Jehle and W. C. Parke, Phys. Rev. 137, B760 (1965)

[c1] G. Parravicini, A. Sparzani, and M. Pauri, Nuovo Cimento Letters 1, 295 (1969)

[c2] G. Parravicini and A. Sparzani, University of Milan Report No. FUM 0/103/FT, 1969 (unpublished)

[c3] I. M. Gel'fand, R. A. Minlos, and Z. Ya. Shapiro, Representations of the Rotation and Lorentz Groups and Their Applications (Oxford U. P., London, 1963)

[c4] L. L. Foldy, Phys. Rev. 102, 568 (1956)

[c5] L. L. Foldy and S. A. Wouthuysen, Phys. Rev. 78, 29 (1950)

[c6] E. P. Wigner, Ann. Math. 40, 149 (1939)

[c7] V. Bargmann and E. P. Wigner, Proc. Natl. Acad. Sci. U. S. 34, 211 (1948)

[c8] Yu. M. Shirokov, Zh. Eksperim. i Teor. Fiz. 33, 861 (1957) ibid.33, 1196 (1957) ibid.33, 1208 (1957) Soviet Phys. JETP 6, 664 (1958) Soviet Phys. JETP6, 919 (1958) Soviet Phys. JETP6, 929 (1958)

[c9] A. S. Wightman, in Dispersion Relations and Elementary Particles, Les Houches (Hermann, Paris, 1960), p. 159

[c10] H. Joos, Fortschr. Physik 10, 65 (1962)

[c11] R. Shaw, Nuovo Cimento 33, 1074 (1964)

[c12] S. Weinberg, Phys. Rev. 133, B1318 (1964)

[c13] P. Moussa and R. Stora, in Boulder Lectures in Theoretical Physics, edited by W. E. Brittin and A. O. Barut (Colorado U. P., Boulder, 1965), Vol. VIIA, p. 37

[c14] ([15]) and ([16])

[c15] P. Winternitz, Rutherford Laboratory Report No. RPP/T/3, 1969 (unpublished)

[c16] A. P. Balachandran, Syracuse University Report No. NYO-3399-272, SU-7206-272, 1969 (unpublished)

[c17] C. Fronsdal, Phys. Rev. 113, 1367 (1959)

[c18] D. L. Weaver, C. L. Hammer, and R. H. Good, Jr., Phys. Rev. 135, B241 (1964)

[c19] D. L. Pürsey, Ann. Phys. (N.Y.) 32, 157 (1965)

[c20] W. K. Tung, Phys. Rev. 156, 1385 (1967)

[c21] Omitted endnote

[c22] A. Chakrabarti, J. Math. Phys. 4, 1215 (1963)

[c23] J. Sesma, J. Math. Phys. 7, 1300 (1966)

[c24] J. A. De Azcarraga and L. J. Boya, J. Math. Phys. 9, 1689 (1968)

[c25] J. A. De Azcarraga and L. Oliver, J. Math. Phys. 10, 1869 (1969)

[c26] [11]

[c27] Sec. III of [19]

[c28] [22]

[c29] ([22–24,30])

[c30] A. Chakrabarti, J. Math. Phys. 4, 1223 (1963)

[c31] A. Chakrabarti, J. Math. Phys. 7, 949 (1966)

[c32] J. J. Giambiagi, Nuovo Cimento 16, 202 (1960)

[c33] C. G. Bollini and J. J. Giambiagi, Nuovo Cimento 21, 107 (1961)

[c34] R. H. Good, Jr. and M. E. Rose, Nuovo Cimento 24, 864 (1962)

[c35] H. Jehle and W. C. Parke, Phys. Rev. 137, B760 (1965)

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Realizations of Representations of the Poincaré Group and Associated Similarity Transformations

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