Group theory for physicists

Group Theory for Physicists

Volumn , Issue , 2007, Pages 1-491

  Ma, Zhong Qi ^a  

^a INSTITUTE OF HIGH ENERGY PHYSICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84967662782     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/6596     Document Type: Book

References (88)

1. Adams, B. G., Cizek, J. and Paldus, J. (1987). Lie algebraic methods and their applications to simple quantum systems, Advances in Quantum Chemistry, Vol. 19, Academic Press, New York.
2. Andrews, G. E. (1976). The Theory of Partitions, Encyclopedia of Mathematics and Its Applications, Vol. 2, Ed. Gian-Carlo Rota, Addison-Wesley.
3. Bayman, B. F. (1960). Some Lectures on Groups and their Applications to Spectroscopy, Nordita.
4. Berenson, R. and Birman, J. L. (1975). Clebsch-Gordan coefficients for crystal space group, J. Math. Phys. 16, 227.
5. Biedenharn, L. C., Giovannini, A. and Louck, J. D. (1970). Canonical definition of Wigner coefficients in U(n), J. Math. Phys. 11, 2368.
6. Biedenharn, L. C. and Louck, J. D. (1981). Angular Momentum in Quantum Physics, Theory and Application, Encyclopedia of Mathematics and its Ap-plication, Vol. 8, Ed. G. C. Rota, Addison-Wesley, Massachusetts.
7. Bjorken, J. D. and Drell, S. D. (1964). Relativistic Quantum Mechanics, McGraw-Hill Book Co., New York.
8. Boerner, H. (1963). Representations of Groups, North-Holland, Amsterdam.
9. Bourbaki, N. (1989). Elements of Mathematics, Lie Groups and Lie Algebras, Springer-Verlag, New York.
10. Bradley, C. J. and Cracknell, A. P. (1972). The Mathematical Theory of Symmetry in Solids, Clarendon Press, Oxford.
11. Bremner, M. R., Moody, R. V. and Patera, J. (1985). Tables of Dominant Weight Multiplicities for Representations of Simple Lie Algebras, Pure and Applied Mathematics, A Series of Monographs and Textbooks 90, Marcel Dekker, New York.
12. Burns, G. and Glazer, A. M. (1978). Space Groups for Solid State Scientists, Academic Press, New York.
13. Chen, J. Q., Wang, P. N., Lu Z. M. and Wu, X. B. (1987). Tables of the Clebsch-Gordan, Racah and Subduction Coefficients of SU(n) Groups, World Scientific, Singapore.
14. Chen, J. Q., Ping, J. L. and Wang, F. (2002). Group Representation Theory for Physicists, 2nd edition, World Scientific, Singapore.
15. Chen, J. Q. and Ping, J. L. (1997). Algebraic expressions for irreducible bases of icosahedral group, J. Math. Phys. 38, 387.
16. Cotton, F. A. (1971). Chemical Applications of Group Theory, Wiley, New York.
17. de Swart, J. J. (1963). The octet model and its Clebsch-Gordan coefficients, Rev. Mod. Phys. 35, 916.
18. Dai A. Y. (1983). A graphic rule for dimensions of irreducible spinor representations of SO(N), J. Lanzhou Univ. (Natural Sciences) 19, № 2, 33 (in Chinese).
19. Deng Y. F. and Yang, C. N. (1992). Eigenvalues and eigenfunctions of the Hückel Hamiltonian for Carbon-60, Phys. Lett. A 170, 116.
20. Dirac, P. A. M. (1958). The Principle of Quantum Mechanics, Clarendon Press, Oxford.
21. Dong, S. H., Hou, X. W. and Ma, Z. Q. (1998a). Irreducible bases and correlations of spin states for double point groups, Inter. J. Theor. Phys. 37, 841.
22. Dong, S. H., Xie, M. and Ma, Z. Q. (1998b). Irreducible bases in icosahedral group space, Inter. J. Theor. Phys. 37, 2135.
23. Dong, S. H., Hou, X. W. and Ma, Z. Q. (1998c). Relativistic Levinson theorem in two dimensions, Phys. Rev. A 58, 2160.
24. Dong, S. H., Hou, X. W. and Ma, Z. Q. (2001). Correlations of spin states for icosahedral double group, Inter. J. Theor. Phys. 40, 569.
25. Dong, S. H. and Ma, Z. Q. (2003). Exact solutions to the Dirac equation with a Coulomb potential in 2 + 1 dimensions, Phys. Lett. A 312, 78.
26. Duan, B., Gu, X. Y. and Ma, Z. Q. (2001). Precise calculation for energy levels of a helium atom in P states, Phys. Lett. A 283, 229.
27. Duan, B., Gu, X. Y. and Ma, Z. Q. (2002). Numerical calculation of energies of some excited states in a helium atom, Eur. Phys. J. D 19, 9.
28. Dynkin, E. B. (1947). The structure of semisimple algebras, Usp. Mat. Nauk. (N. S.), 2, 59. Transl. in Am. Math. Soc. Transl. (I), 9, 308, 1962.
29. Eckart, C. (1934). The kinetic energy of polyatomic molecules, Phys. Rev. 46, 383.
30. Edmonds, A. R. (1957). Augular Momentum in Quantum Mechanics, Princeton University Press, Princeton.
31. Elliott J. P. and Dawber, P. G. (1979). Symmetry in Physics, McMillan Press, London.
32. Feng Kang (1991). The Hamiltonian way for computing Hamiltonian dynamics, Applied and Industrial Mathematics, Ed. R. Spigler, Kluwer Academic Publishers, p. 17.
33. Fronsdal, C. (1963). Group theory and applications to particle physics, 1962, Brandies Lectures, Vol. 1, 427. Ed. K. W. Ford, Benjamin, New York.
34. Gao, S. S. (1992). Group Theory and its Applications in Particle Physics, Higher Education Press, Beijing (in Chinese).
35. Gel’fand, I. M., Minlos, R. A. and Shapiro, Z. Ya. (1963). Representations of the Rotation and Lorentz Groups and Their Applications, Transl. from Russian by G. Cummins and T. Boddington, Pergamon Press, New York.
36. Gel’fand, I. M. and Zetlin, M. L. (1950). Matrix Elements for the Unitary Groups, Dokl. Akad. Nauk 71, 825.
37. Gell-Mann, M. and Ne’eman, Y. (1964). The EightfoldWay, Benjamin, New York.
38. Georgi, H. (1982). Lie Algebras in Particle Physics, Benjamin, New York.
39. Gilmore, R. (1974). Lie Groups, Lie Algebras and Some of Their Applications, Wiley, New York.
40. Gu, X. Y., Duan, B. and Ma, Z. Q. (2001a). Conservation of angular momentum and separation of global rotation in a quantum N-body system, Phys. Lett. A 281, 168.
41. Gu, X. Y., Duan, B. and Ma, Z. Q. (2001b). Independent eigenstates of angular momentum in a quantum N-body system, Phys. Rev. A 64, 042108(1-14).
42. Gu, X. Y., Duan, B. and Ma, Z. Q. (2001c). Quantum three-body system in D dimensions, J. Math. Phys. 43, 2895.
43. Gu, X. Y., Ma, Z. Q. and Dong, S. H. (2002). Exact solutions to the Dirac equation for a Coulomb potential in D+1 dimensions, Inter. J. Mod. Phys. E 11, 335.
44. Gu, X. Y., Ma, Z. Q. and Duan, B. (2003a). Interdimensional degeneracies for a quantum three-body system in D dimensions, Phys. Lett. A 307, 55.
45. Gu, X. Y., Ma, Z. Q. and Sun, J. Q. (2003b). Quantum four-body system in D dimensions, J. Math. Phys. 44, 3763.
46. Gu, X. Y., Ma, Z. Q. and Sun, J. Q. (2003c). Interdimensional degeneracies in a quantum isolated four-body system, Phys. Lett. A 314, 156.
47. Gu, X. Y., Ma, Z. Q. and Sun, J. Q. (2003d). Interdimensional degeneracies in a quantum N-body system, Europhys. Lett. 64, 586.
48. Gu, X. Y., Ma, Z. Q. and Dong, S. H. (2003e). The Levinson theorem for the Dirac equation in D + 1 dimensions, Phys. Rev. A 67, 062715(1-12).
49. Hamermesh, M. (1962). Group Theory and its Application to Physical Problems, Addison-Wesley, Massachusetts.
50. Han, Q. Z. and Sun, H. Z. (1987). Group Theory, Peking University Press, Beijing (in chinese).
51. Heine, V. (1960). Group Theory in Quantum Mechanics, Pergamon Press, London.
52. Hirschfelder, J. O. and Wigner, E. P. (1935). Separation of rotational coordinates from the Schrödinger equation for N particles, Proc. Natl. Acad. Sci. U.S.A. 21, 113.
53. Hou, Bo-Yu, Hou, Bo-Yuan and Ma Z. Q. (1990a). Clebsch-Gordan coefficients, Racah coefficients and braiding fusion of quantum s`(2) enveloping algebra I, Commun. Theor. Phys. 13, 181.
54. Hou, Bo-Yu, Hou, Bo-Yuan and Ma Z. Q. (1990b). Clebsch-Gordan coefficients, Racah coefficients and braiding fusion of quantum s`(2) enveloping algebra II, Commun. Theor. Phys. 13, 341.
55. Hou, Bo-Yuan and Hou, Bo-Yu (1997). Differential Geometry for Physicists, World Scientific, Singapore.
56. Hou, X. W., Xie, M., Dong, S. H. and Ma, Z. Q. (1998). Overtone spectra and intensities of tetrahedral molecules in boson-realization models, Ann. Phys. (N.Y.) 263, 340.
57. Hsiang, W. T. and Hsiang, W. Y. (1998). On the reduction of the Schrödinger’s equation of three-body problem to a system of linear algebraic equations, preprint.
58. Hsiang, W. Y. (1998). On the kinematic geometry of many body system, preprint.
59. Itzykson, C. and Nauenberg, M. (1966). Unitary groups: Representations and decompositions, Rev. Mod. Phys. 38, 95.
60. Joshi, A. W. (1977). Elements of Group Theory for Physicists, Wiley.
61. Kazdan, D. and Lusztig, G. (1979). Representations of Coxeter groups and Hecke algebras, Invent. Math. 53, 165.
62. Koster, G. F. (1957). Space Groups and Their Representations in Solid State Physics, Eds. F. Seitz and D. Turnbull, Academic Press, New York, 5, 174.
63. Kovalev, O. V. (1961). Irreducible Representations of Space Groups, translated from Russian by A. M. Gross, Gordon & Breach.
64. Lipkin, H. J. (1965). Lie Groups for Pedestrians, North-Holland, Amsterdam.
65. Littlewood, D. E. (1958). The Theory of Group Characters, Oxford University Press, Oxford.
66. Liu, F., Ping, J. L. and Chen, J. Q. (1990). Application of the eigenfunction method to the icosahedral group, J. Math. Phys. 31, 1065.
67. Ma, Z. Q. (1993). Yang-Baxter Equation and Quantum Enveloping Algebras, World Scientific, Singapore.
68. Ma, Z. Q. and Dai, A. Y. (1982). A graphic rule for dimensions of irreducible tensor representations of SO(N), J. Lanzhou Univ. (Natural Sciences) 18, № 2, 97 (in Chinese).
69. Ma, Z. Q. and Gu, X. Y. (2004). Problems & Solutions in Group Theory for Physicists, World Scientific, Singapore.
70. Ma, Z. Q., Hou, X. W. and Xie, M. (1996). Boson-realization model for the vibrational spectra of tetrahedral molecules, Phys. Rev. A 53, 2173.
71. Marshak, R. E., Riazuddin, and Ryan, C. P. (1969). Theory of Weak Interactions in Particle Physcs, John Wiley & Sons, Inc., New York.
72. Miller, Jr. W., (1972). Symmetry Groups and Their Applications, Academic Press, New York.
73. Racah, G. (1951). Group Theory and Spectroscopy, Lecture Notes in Princeton.
74. Ren S. Y. (2006). Electronic States in Crystals of Finite Size, Quantum confinement of Bloch waves, Springer, New York (2006).
75. Roman, P. (1964). Theory of Elementary Particles, North-Holland, Amsterdam.
76. Rose, M. E. (1957). Elementary Theory of Angular Momentum, Wiley, New York.
77. Salam, A. (1963). The Formalism of Lie Groups, in Theoretical Physics, Director: A. Salam, International Atomic Energy Agency, Vienna, 173.
78. Schiff, L. I. (1968). Quantum Mechanics, Third Edition, McGraw-Hill, New York.
79. Serre, J. P. (1965). Lie Algebras and Lie Groups, Benjamin, New York.
80. Tinkham, M. (1964). Group Theory and Quantum Mechanics, McGraw-Hill, New York.
81. Tong, D. M., Zhu, C. J. and Ma, Z. Q. (1992). Irreducible representations of braid groups, J. Math. Phys. 33, 2660.
82. Tung, W. K. (1985). Group Theory in Physics, World Scientific, Singapore.
83. Weyl, H. (1931). The Theory of Groups and Quantum Mechanics, translated from German by H. P. Robertson, Dover Publications.
84. Weyl, H. (1946). The Classical Groups, Princeton University Press, Princeton.
85. Wigner, E. P. (1959). Group Theory and its Applications to the Quantum Mechanics of Atomic Spectra, Academic Press, New York.
86. Wybourne, B. G. (1974). Classical Groups for Physicists, Wiley, New York.
87. Yamanouchi, T. (1937). On the construction of unitary irreducible representation of the symmetric group, Proc. Phys. Math. Soc. Jpn 19, 436.
88. Zou, P. C. and Huang, Y. C. (1995). Proof of "irreducible postulation" and its applications, High Ener. Phys. Nucl. Phys. 19, 375.