Wigner rotations, Bargmann invariants and geometric phases

Journal of Physics A: Mathematical and General

Volumn 36, Issue 9, 2003, Pages 2347-2370

  Mukunda, N ^a,b   Aravind, P K ^c   Simon, R ^d  

^a INDIAN INSTITUTE OF SCIENCE   (India)

^b JAWAHARLAL NEHRU CENTRE FOR ADVANCED SCIENTIFIC RESEARCH   (India)

^c WORCESTER POLYTECHNIC INSTITUTE   (United States)

^d INSTITUTE OF MATHEMATICAL SCIENCES   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037424583     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/36/9/312     Document Type: Article

References (40)

1. A very readable account of these subjects, with much history, may be found in Tomonaga S-I 1997 The Story of Spin (Chicago: University of Chicago Press) Wigner's original paper on the unitary representations of the inhomogeneous Lorentz group is Wigner E P 1939 Ann. Math. 40 149 This is reprinted in Dyson F J 1966 Symmetry Groups in Nuclear and Particle Physics (New York: Benjamin)
2. A very readable account of these subjects, with much history, may be found in Tomonaga S-I 1997 The Story of Spin (Chicago: University of Chicago Press) Wigner's original paper on the unitary representations of the inhomogeneous Lorentz group is Wigner E P 1939 Ann. Math. 40 149 This is reprinted in Dyson F J 1966 Symmetry Groups in Nuclear and Particle Physics (New York: Benjamin)
3. A very readable account of these subjects, with much history, may be found in Tomonaga S-I 1997 The Story of Spin (Chicago: University of Chicago Press) Wigner's original paper on the unitary representations of the inhomogeneous Lorentz group is Wigner E P 1939 Ann. Math. 40 149 This is reprinted in Dyson F J 1966 Symmetry Groups in Nuclear and Particle Physics (New York: Benjamin)
4. Out of an extensive list of references, we may mention a few recent ones Van Wyk C B 1984 Am. J. Phys. 52 853 Ben-Menachem A 1985 Am. J. Phys. 53 62 Strandberg M W P 1986 Phys. Rev. A 34 2458 Rowe E G P 1996 Am. J. Phys. 64 1184 Aravind P K 1997 Am. J. Phys. 65 634 Aravind P K 1990 Phys. Rev. A 42 4077
5. Out of an extensive list of references, we may mention a few recent ones Van Wyk C B 1984 Am. J. Phys. 52 853 Ben-Menachem A 1985 Am. J. Phys. 53 62 Strandberg M W P 1986 Phys. Rev. A 34 2458 Rowe E G P 1996 Am. J. Phys. 64 1184 Aravind P K 1997 Am. J. Phys. 65 634 Aravind P K 1990 Phys. Rev. A 42 4077
6. Out of an extensive list of references, we may mention a few recent ones Van Wyk C B 1984 Am. J. Phys. 52 853 Ben-Menachem A 1985 Am. J. Phys. 53 62 Strandberg M W P 1986 Phys. Rev. A 34 2458 Rowe E G P 1996 Am. J. Phys. 64 1184 Aravind P K 1997 Am. J. Phys. 65 634 Aravind P K 1990 Phys. Rev. A 42 4077
7. Out of an extensive list of references, we may mention a few recent ones Van Wyk C B 1984 Am. J. Phys. 52 853 Ben-Menachem A 1985 Am. J. Phys. 53 62 Strandberg M W P 1986 Phys. Rev. A 34 2458 Rowe E G P 1996 Am. J. Phys. 64 1184 Aravind P K 1997 Am. J. Phys. 65 634 Aravind P K 1990 Phys. Rev. A 42 4077
8. Out of an extensive list of references, we may mention a few recent ones Van Wyk C B 1984 Am. J. Phys. 52 853 Ben-Menachem A 1985 Am. J. Phys. 53 62 Strandberg M W P 1986 Phys. Rev. A 34 2458 Rowe E G P 1996 Am. J. Phys. 64 1184 Aravind P K 1997 Am. J. Phys. 65 634 Aravind P K 1990 Phys. Rev. A 42 4077
9. Out of an extensive list of references, we may mention a few recent ones Van Wyk C B 1984 Am. J. Phys. 52 853 Ben-Menachem A 1985 Am. J. Phys. 53 62 Strandberg M W P 1986 Phys. Rev. A 34 2458 Rowe E G P 1996 Am. J. Phys. 64 1184 Aravind P K 1997 Am. J. Phys. 65 634 Aravind P K 1990 Phys. Rev. A 42 4077
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17. Chiao R Y and Jordan T F 1988 Phys. Lett. A 132 77 Han D, Hardekopf E E and Kim Y S 1989 Phys. Rev. A 39 1269 Gerry C C 1989 Phys. Rev. A 39 3204 Jordan T F 1988 J. Math. Phys. 29 2042 Kitano M and Yabuzaki T 1989 Phys. Lett. A 142 321 Agarwal G S 1991 Opt. Commun. 82 213
18. Chiao R Y and Jordan T F 1988 Phys. Lett. A 132 77 Han D, Hardekopf E E and Kim Y S 1989 Phys. Rev. A 39 1269 Gerry C C 1989 Phys. Rev. A 39 3204 Jordan T F 1988 J. Math. Phys. 29 2042 Kitano M and Yabuzaki T 1989 Phys. Lett. A 142 321 Agarwal G S 1991 Opt. Commun. 82 213
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26. A comprehensive reference to this group and its relation to the Lorentz group is Gel'fand I M, Minlos R A and Shapiro Z Ya 1963 Representations of the Rotation and Lorentz Groups and their Applications (New York: Macmillan)
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31. This has been used in Chaturvedi S and Mukunda N 2001 Int. J. Mod. Phys. A 16 1481 A complete derivation may be found in Mukunda N, Arvind, Chaturvedi S and Simon R 2001 Phys. Rev. A 65 012102
32. This has been used in Chaturvedi S and Mukunda N 2001 Int. J. Mod. Phys. A 16 1481 A complete derivation may be found in Mukunda N, Arvind, Chaturvedi S and Simon R 2001 Phys. Rev. A 65 012102
33. The modern theory of the GP was first presented in Berry M V 1984 Proc. R. Soc. A 392 45 Early advances and applications are summarized and collected in Shapere A and Wilczek F 1989 Geometric Phases in Physics (Singapore: World Scientific) A survey and a collection of a large number of references on geometric phases can be found in Anandan J, Christian J and Wanelik K 1997 Resource letter GPP-1: geometric phases in physics Am. J. Phys. 65 180
34. The modern theory of the GP was first presented in Berry M V 1984 Proc. R. Soc. A 392 45 Early advances and applications are summarized and collected in Shapere A and Wilczek F 1989 Geometric Phases in Physics (Singapore: World Scientific) A survey and a collection of a large number of references on geometric phases can be found in Anandan J, Christian J and Wanelik K 1997 Resource letter GPP-1: geometric phases in physics Am. J. Phys. 65 180
35. The modern theory of the GP was first presented in Berry M V 1984 Proc. R. Soc. A 392 45 Early advances and applications are summarized and collected in Shapere A and Wilczek F 1989 Geometric Phases in Physics (Singapore: World Scientific) A survey and a collection of a large number of references on geometric phases can be found in Anandan J, Christian J and Wanelik K 1997 Resource letter GPP-1: geometric phases in physics Am. J. Phys. 65 180
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