Momentum projection of solitons including quantum corrections
The method of projection is applied to a relativistic field theory of fermions interacting with a nonlinear scalar field, specifically the Friedberg-Lee soliton model. Projection is effected by operating on a localized “bag” state with the translation operator exp (iP·Z), and integrating overZ. The resulting state is an eigenstate of zero momentum. The energy and the expectation value of other physical operators can be expressed as Gaussian moments of the Hamiltonian or the physical operator times powers of the momentum operator taken with respect to the bag state. Renormalization in the one-loop approximation is discussed in detail for the boson sector, and briefly for the fermion sector. The method can be tested for convergence against nonexpansion techniques. The latter, however, cannot so easily handle distortion of the Bose modes or the distortion of the Dirac sea.
KeywordsSoliton Physical Operator Scalar Field Quantum Correction Relativistic Field
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- 1.D. L. Hill and J. A. Wheeler,Phys. Rev. 89, 1106 (1953); J. J. Griffin and J. A. Wheeler,Phys. Rev. 108, 311 (1957); R. E. Peierls and J. Yoccoz,Proc. Phys. Soc. London A 70, 381 (1957).Google Scholar
- 2.J-L. Dethier, R. Goldflam, E. M. Henley, and L. Wilets,Phys. Rev. D 27, 2193 (1983).Google Scholar
- 3.G. Lübeck, M. C. Birse, E. M. Henley, and L. Wilets,Phys. Rev. D 33, 234 (1986).Google Scholar
- 4.R. Goldflam and L. Wilets,Phys. Rev. D 25, 1951 (1982).Google Scholar
- 5.R. Jackiw,Rev. Mod. Phys. 49, 681 (1977); R. Rajaraman,Solitons and Instantons (NorthHolland, Amsterdam, 1982).Google Scholar
- 6.C. G. Callan and D. J. Gross,Nucl. Phys. B 93, 29 (1975).Google Scholar
- 7.R. Friedberg and T. D. Lee,Phys. Rev. D 15, 1694 (1977);16, 1096 (1977);18, 2623 (1978); T. D. Lee,Particle Physics and Introduction to Field Theory (Harwood Academic, New York, 1981).Google Scholar
- 8.L. Wilets, “Quark Models of Hadronic Interactions” inHadrons and Heavy Ions (Springer-Verlag, New York, 1985).Google Scholar
- 9.J. M. Cornwall, R. Jackiw, and E. Tomboulis,Phys. Rev. D 10, 2428 (1974); S. Coleman, R. Jackiw, and H. Politzer,Phys. Rev. D 10, 2491 (1974); S.-J. Chang,Phys. Rev. D 12, 1071 (1975); T. Barnes and G. I. Ghandour,Phys. Rev. D 22, 924 (1980).Google Scholar
- 10.E. H. Wichmann and N. M. Kroll,Phys. Rev. 101, 843 (1956); M. Gyulassy,Nucl. Phys. A 244, 497 (1975).Google Scholar
- 11.G. A. Rinker and L. Wilets,Phys. Rev. A 12, 748 (1975).Google Scholar