<span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo>(</mo><mn>3</mn><mo>)</mo><mn></mn></math></span> Symmetry and Algebraic Realizations of Chiral Symmetry

L. R. Ram Mohan

doi:10.1103/PhysRevD.2.299

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$SU (3)$ Symmetry and Algebraic Realizations of Chiral Symmetry

L. R. Ram Mohan

Department of Physics, Purdue University, Lafayette, Indiana 47907

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Phys. Rev. D 2, 299 – Published 15 July, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.299

Abstract

The algebraic realizations of chiral symmetry obtained by Weinberg are investigated for the case of $SU (3)$ symmetry. When only $p$ -wave interactions are taken into account, the algebraic realization of the first superconvergence condition is given by the Lie algebra of the group $SU (2) \otimes SU (6)$ . The mass matrix obtained from the second superconvergence relation corresponds to degenerate masses within each of the multiplets ( $V = 0, 56$ ) and ( $V = 2, 56$ ). The consequences of particle classification under the group $SU (2) \otimes SU (6)$ are enumerated.

References (15)

S. Weinberg, Phys. Rev. 177, 2604 (1969) Phys. Rev. Letters 22, 1023 (1969)
C. Cronstrom and M. Noga, Nucl. Phys. B15, 61 (1970) M. Noga and C. Cronstrom, Phys. Rev. D 1, 2414 (1970)
B. W. Lee, Phys. Rev. Letters 14, 676 (1965)
C. L. Cook and G. Murtaza, Nuovo Cimento 39, 532 (1965)
J. C. Carter and J. J. Coyne, J. Math. Phys. 10, 1204 (1969)
J. J. deSwart, Rev. Mod. Phys. 35, 916 (1963)
Particle Data Group, Rev. Mod. Phys. 41, 109 (1969)
H. Harari, rapporteur talk, in Proceedings of the Fourteenth International Conference on High Energy Physics, Vienna, Austria, 1968 (CERN, Geneva, 1968), p. 195
J. J. J. Kokkedee, The Quark Model (Benjamin, New York, 1969)
A. Pais, Phys. Rev. Letters 13, 175 (1964) F. Gürsey, A. Pais, and L. A. Radicati, ibid. 13, 299 (1964)
J. G. Kuriyan and E. C. G. Sudarshan, Phys. Letters 21, 106 (1966) Phys. Rev. 162, 1650 (1967)
K. Johnson and S. B. Treiman, Phys. Rev. Letters 14, 189 (1965)
P. Carruthers, Introduction to Unitary Symmetry (Interscience, New York, 1966), Chap. 7
K. T. Mahantappa and E. C. G. Sudarshan, Phys. Rev. Letters 14, 165 (1965)
T. Cook, C. J. Goebel, and B. Sakita, Phys. Rev. Letters 15, 35 (1965)

[c1] S. Weinberg, Phys. Rev. 177, 2604 (1969) Phys. Rev. Letters 22, 1023 (1969)

[c2] C. Cronstrom and M. Noga, Nucl. Phys. B15, 61 (1970) M. Noga and C. Cronstrom, Phys. Rev. D 1, 2414 (1970)

[c3] B. W. Lee, Phys. Rev. Letters 14, 676 (1965)

[c4] C. L. Cook and G. Murtaza, Nuovo Cimento 39, 532 (1965)

[c5] J. C. Carter and J. J. Coyne, J. Math. Phys. 10, 1204 (1969)

[c6] J. J. deSwart, Rev. Mod. Phys. 35, 916 (1963)

[c7] Particle Data Group, Rev. Mod. Phys. 41, 109 (1969)

[c8] H. Harari, rapporteur talk, in Proceedings of the Fourteenth International Conference on High Energy Physics, Vienna, Austria, 1968 (CERN, Geneva, 1968), p. 195

[c9] J. J. J. Kokkedee, The Quark Model (Benjamin, New York, 1969)

[c10] A. Pais, Phys. Rev. Letters 13, 175 (1964) F. Gürsey, A. Pais, and L. A. Radicati, ibid. 13, 299 (1964)

[c11] J. G. Kuriyan and E. C. G. Sudarshan, Phys. Letters 21, 106 (1966) Phys. Rev. 162, 1650 (1967)

[c12] K. Johnson and S. B. Treiman, Phys. Rev. Letters 14, 189 (1965)

[c13] P. Carruthers, Introduction to Unitary Symmetry (Interscience, New York, 1966), Chap. 7

[c14] K. T. Mahantappa and E. C. G. Sudarshan, Phys. Rev. Letters 14, 165 (1965)

[c15] T. Cook, C. J. Goebel, and B. Sakita, Phys. Rev. Letters 15, 35 (1965)

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SU(3) Symmetry and Algebraic Realizations of Chiral Symmetry

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$SU (3)$ Symmetry and Algebraic Realizations of Chiral Symmetry