Feynman Rules for an <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo>(</mo><mn>4</mn><mo>)</mo><mn></mn></math></span> Family with No Ghosts

Ngee-Pong Chang; Charles A. Nelson

doi:10.1103/PhysRevD.2.959

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Feynman Rules for an $O (4)$ Family with No Ghosts

Ngee-Pong Chang and Charles A. Nelson

Physics Department, City College of the City University of New York, New York, New York 10031

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Phys. Rev. D 2, 959 – Published 15 September, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.959

Abstract

When a resonance is observed in an experiment, it is usually assumed that the resonance has a definite spin $J$ . Should, however, an $O (4)$ family of Regge trajectories hit the physical region, we could expect to see a family of resonances of different spins roughly degenerate in energy. For such a family of resonances, there should presumably be a master field which contains all the spins in the family and which interacts as a unit with other hadrons. In this paper we discuss the general tensor construction of such multispin fields. We believe that the splitting of the $A_{2}$ meson is a manifestation of a master field and, in a following paper, study the phenomenology of the $O (4)$ resonance system.

References (23)

M. Toller, Nuovo Cimento 54A, 295 (1968)
D. Z. Freedman and J. M. Wang, Phys. Rev. 160, 1560 (1967)
G. Domokos, Phys. Rev. 159, 1387 (1967)
H. Harari, in Proceedings of the Fourteenth International Conference on High-Energy Physics, Vienna, 1968, edited by J. Prentki and J. Steinberger (CERN, Geneva, 1968)
G. Veneziano, Nuovo Cimento 57A, 190 (1968)
S. Fubini and G. Veneziano, Nuovo Cimento 64A, 811 (1969)
K. Bardakci and S. Mandelstam, Phys. Rev. 184, 1640 (1969)
Y. Nambu, in Proceedings of the International Conference on Symmetries and Quark Models, Wayne State University, 1969 (unpublished)
L. Susskind, Phys. Rev. Letters 23, 545 (1969) Phys. Rev. D 1, 1182 (1970)
C. Zemach, Phys. Rev. 140, B97 (1965)
Omitted endnote
N. P. Chang and C. A. Nelson, Phys. Rev. 2, 966 (1970)
S. Weinberg, Phys. Rev. 133, B1318 (1964) ibid.181, 1893 (1969)
M. D. Scadron, Phys. Rev. 165, 1640 (1968)
H. F. Jones, Nuovo Cimento 59A, 81 (1969)
A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. P., Princeton, N. J., 1957)
R. Delbourgo, K. Koller, and R. M. Williams, J. Math. Phys. 10, 957 (1969)
([15]) Y. Iwasaki, Phys. Rev. 173, 1608 (1968)
Bateman Manuscript Project, Higher Transcendental Functions (McGraw-Hill, New York, 1953), Vol. II, Sec. 10.9
[19], Vol. I
[12] W. K. Tung, Phys. Rev. 156, 1385 (1967)
F. Gürsey and L. A. Radicati, Phys. Rev. Letters 13, 173 (1964) A. Pais, ibid. 13, 175 (1964) F. Gürsey, A. Pais, and L. A. Radicati, ibid. 13, 299 (1964) B. Sakita, ibid. 13, 643 (1964) Phys. Rev. 136, B1759 (1964) A. Salam, R. Delbourgo, and J. Strathdee, Proc. Roy. Soc. (London) A284, 146 (1965)
J. Schwinger, Phys. Rev. 140, B158 (1965) S. J. Chang, 178, 2421 (1969)

[c1] M. Toller, Nuovo Cimento 54A, 295 (1968)

[c2] D. Z. Freedman and J. M. Wang, Phys. Rev. 160, 1560 (1967)

[c3] G. Domokos, Phys. Rev. 159, 1387 (1967)

[c4] H. Harari, in Proceedings of the Fourteenth International Conference on High-Energy Physics, Vienna, 1968, edited by J. Prentki and J. Steinberger (CERN, Geneva, 1968)

[c5] G. Veneziano, Nuovo Cimento 57A, 190 (1968)

[c6] S. Fubini and G. Veneziano, Nuovo Cimento 64A, 811 (1969)

[c7] K. Bardakci and S. Mandelstam, Phys. Rev. 184, 1640 (1969)

[c8] Y. Nambu, in Proceedings of the International Conference on Symmetries and Quark Models, Wayne State University, 1969 (unpublished)

[c9] L. Susskind, Phys. Rev. Letters 23, 545 (1969) Phys. Rev. D 1, 1182 (1970)

[c10] C. Zemach, Phys. Rev. 140, B97 (1965)

[c11] Omitted endnote

[c12] N. P. Chang and C. A. Nelson, Phys. Rev. 2, 966 (1970)

[c13] S. Weinberg, Phys. Rev. 133, B1318 (1964) ibid.181, 1893 (1969)

[c14] M. D. Scadron, Phys. Rev. 165, 1640 (1968)

[c15] H. F. Jones, Nuovo Cimento 59A, 81 (1969)

[c16] A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. P., Princeton, N. J., 1957)

[c17] R. Delbourgo, K. Koller, and R. M. Williams, J. Math. Phys. 10, 957 (1969)

[c18] ([15]) Y. Iwasaki, Phys. Rev. 173, 1608 (1968)

[c19] Bateman Manuscript Project, Higher Transcendental Functions (McGraw-Hill, New York, 1953), Vol. II, Sec. 10.9

[c20] [19], Vol. I

[c21] [12] W. K. Tung, Phys. Rev. 156, 1385 (1967)

[c22] F. Gürsey and L. A. Radicati, Phys. Rev. Letters 13, 173 (1964) A. Pais, ibid. 13, 175 (1964) F. Gürsey, A. Pais, and L. A. Radicati, ibid. 13, 299 (1964) B. Sakita, ibid. 13, 643 (1964) Phys. Rev. 136, B1759 (1964) A. Salam, R. Delbourgo, and J. Strathdee, Proc. Roy. Soc. (London) A284, 146 (1965)

[c23] J. Schwinger, Phys. Rev. 140, B158 (1965) S. J. Chang, 178, 2421 (1969)

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Feynman Rules for an $O (4)$ Family with No Ghosts

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Feynman Rules for an O(4) Family with No Ghosts

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References (23)

Feynman Rules for an $O (4)$ Family with No Ghosts