Poincaré-invariant Lee model

Michael G. Fuda

doi:10.1103/PhysRevD.41.534

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Poincaré-invariant Lee model

Michael G. Fuda

Department of Physics and Astronomy, State University of New York at Buffalo, Buffalo, New York 14260

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Phys. Rev. D 41, 534 – Published 15 January, 1990

DOI: https://doi.org/10.1103/PhysRevD.41.534

Abstract

A relativistic generalization of the Lee model is developed within the framework of light-front dynamics. The model describes three particles $V$ , $N$ , and $θ$ interacting through the virtual process $V ⇄ N + θ$ , with no antiparticles present. The model consists of ten generators which satisfy the commutation relations of the Poincaré group. The Lorentz invariance of the $S$ -matrix elements that arise is demonstrated. The dressed $V$ -particle state is given, and the integral equations that arise in the $θ V - θ θ N$ sector are derived. The interacting spin operator for the model is analyzed in some detail. The integral equations for the $θ V - θ θ N$ sector are transformed to a new picture and a partial-wave analysis of the transformed equations is carried out. It is shown that the $θ V$ elastic scattering amplitudes can be obtained from the solution of uncoupled, one-dimensional integral equations. The model has many of the features of few-particle systems involving pions and nucleons and moreover provides insight into dealing with the interacting angular momentum operators of light-front dynamics.

References (36)

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[c1] T. D. Lee, Phys. Rev. 95, 1329 (1954)

[c2] R. D. Amado, Phys. Rev. 122, 696 (1961)

[c3] G. Källén and W. Pauli, K. Dan. Vidensk. Selsk. Mat.-Fys. Medd. 30, 7 (1955) K. W. Ford, Phys. Rev. 105, 320 (1957) W. Heisenberg, Nucl. Phys. 4, 532 (1957) B. Ferretti, Nuovo Cimento 12, 393 (1959)

[c4] M. M. Lévy, Nuovo Cimento 13, 115 (1959) ibid.14, 612 (1959)

[c5] R. D. Amado, Phys. Rev. 132, 485 (1963)

[c6] R. D. Amado, Phys. Rev. 14, 902 (1966) R. Aaron, R. D. Amado, and Y. Y. Yam, ibid. 140, B1291 (1965) R. D. Amado, Annu. Rev. Nucl. Sci. 19, 635 (1969)

[c7] Ronald Aaron, Phys. Rev. 151, 1293 (1966)

[c8] M. G. Fuda, Phys. Rev. C 25, 1972 (1982)

[c9] M. G. Fuda, Phys. Rev. C 26, 204 (1982) ibid.29, 1222 (1984)

[c10] M. G. Fuda, Phys. Rev. C 30, 666 (1984)

[c11] G. A. Miller, A. W. Thomas, and S. Théberge, Phys. Lett. 91B, 192 (1980) S. Théberge, A. W. Thomas, and G. A. Miller, Phys. Rev. D 22, 2838 (1980)

[c12] C. Schmit and J.-P. Maillet, Nucl. Phys. A312, 236 (1978) H. R. Petry and M. Sawicki, Z. Naturforsch. 33a, 1 (1978) M. Sawicki and D. Schütte, ibid. 36a, 1261 (1981) M. Sawicki, Phys. Rev. C 27, 1415 (1983)

[c13] P. A. M. Dirac, Rev. Mod. Phys. 21, 392 (1949)

[c14] H. Leutwyler and J. Stern, Ann. Phys. (N.Y.) 112, 94 (1978)

[c15] F. Coester and W. N. Polyzou, Phys. Rev. D 26, 1348 (1982)

[c16] B. de Dormale, J. Math. Phys. 20, 1229 (1979)

[c17] M. Betz and T.-S. H. Lee, Phys. Rev. C 23, 375 (1981) M. Betz and F. Coester, ibid. 21, 2505 (1980)

[c18] S. Schweber, An Introduction to Relativistic Quantum Field Theory (Harper and Row, New York, 1961)

[c19] M. V. Terent'ev, Yad. Fiz. 24, 207 (1976) [Sov. J. Nucl. Phys. 24, 106 (1976)] V. B. Berestetskii and M. V. Terent'ev, Yad. Fiz. 24, 1044 (1976) [Sov. J. Nucl. Phys. 24, 547 (1976)] V. B. BerestetskiiM. V. Terent'evYad. Fiz.25, 653 (1977) [Sov. J. Nucl. Phys. 25, 347 (1977)] L. A. Kondratyuk and M. V. Terent'ev, 31, 1087 (1980) [Sov. J. Nucl. Phys. 31, 561 (1980)] B. L. G. Bakker, L. A. Kondratyuk, and M. V. Terent'ev, Nucl. Phys. B158, 497 (1979)

[c20] M. G. Fuda, Phys. Rev. C 36, 1489 (1987)

[c21] P. L. Chung, F. Coester, B. D. Keister, and W. N. Polyzou, Phys. Rev. C 37, 2000 (1988)

[c22] M. G. Fuda, Ann. Phys. (N.Y.) 197(2), 265 (1990)

[c23] J. L. Basevant and R. L. Omnes, Phys. Rev. Lett. 17, 775 (1966)

[c24] H. Garcilazo and L. Mathelitsch, Phys. Rev. C 28, 1272 (1983) L. Mathelitsch and H. Garcilazo, ibid. 32, 1635 (1985)

[c25] Y. S. Kim and Marilyn E. Noz, Theory and Applications of the Poincaré Group (Reidel, Boston, 1986)

[c26] M. L. Goldberger and S. B. Treiman, Phys. Rev. 113, 1663 (1959)

[c27] M. Stephen Maxon and Richard B. Curtis, Phys. Rev. 137, B996 (1965) M. Stephen Maxon, ibid. 149, 1273 (1966) Leonard M. Scarfone, J. Math. Phys. 7, 159 (1966)

[c28] S. G. Gasiorowicz, Elementary Particle Physics (Wiley, New York, 1966)

[c29] Steven Weinberg, Phys. Rev. 150, 1313 (1966)

[c30] J. B. Bronzan, Phys. Rev. 139, B751 (1965)

[c31] F. S. Chen-Cheung, Phys. Rev. 152, 1408 (1966) J. B. Bronzan, ibid. 172, 1429 (1968)

[c32] H. Chew, Phys. Rev. 132, 2756 (1963)

[c33] H. J. Melosh, Phys. Rev. D 9, 1095 (1974)

[c34] J. M. Namyslowski, Prog. Part. Nucl. Phys. 14, 49 (1984)

[c35] Michael F. Fuda, Phys. Rev. C 25, 226 (1987)

[c36] M. G. Fuda, Phys. Rev. C 31, 1365 (1985) ibid.32, 2024 (1985)

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Poincaré-invariant Lee model

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