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Semiclassical bound-state methods in four-dimensional field theory: Trace identities, mode sums, and renormalization for scalar theories
Phys. Rev. D 14, 1977 – Published 15 October, 1976
DOI: https://doi.org/10.1103/PhysRevD.14.1977
Abstract
Semiclassical and inverse scattering methods, previously restricted to two-dimensional models, are extended to four-dimensional scalar field theories. The necessary trace identities are derived, mode sums are carried out, and renormalization is explicitly demonstrated. The four-dimensional model is used to illustrate these techniques. A renormalized expression for bound-state energies of this model, parametrized by the scattering data of a three-dimensional Schrödinger equation, is obtained. This expression contains nontrivial quantum fluctuation effects, and corresponds to the leading-order term of a expansion. In this model, stable -body bound states do not seem to appear, even though a two-body bound state has been found in a expansion of the Green's functions. Possible reasons for this failure to bind are discussed.
References (10)
- R. Dashen, B. Hasslacher, and A. Neveu, Phys. Rev. D 10, 4114 (1974) ibid.10, 4130 (1974) ibid.10, 4138 (1974) ibid.11, 3424 (1975) ibid.12, 2443 (1975) J. Goldstone and R. Jackiw, ibid. 11, 1486 (1975) A. Klein and F. Krejs, ibid. 12, 3112 (1975) ibid.13, 3282 (1976) ibid.13, 3295 (1976) S.-J. Chang, ibid. 12, 1071 (1975)
- L. F. Abbott, Phys. Rev. D 14, 552 (1976)
- C. R. Nohl, Princeton report (unpublished) D. Campbell, Los Alamos report (unpublished) S. Y. Lee and A. Gavrielides, Phys. Rev. D 12, 3880 (1975) S.-S. Shei, ibid. 14, 535 (1976)
- V. E. Zakharov and L. D. Faddeev, Func. Anal. Appl. 5, 280 (1972) L. D. Faddeev, Trudy Mat. in-ta im. V. A. Steklova 73, 314 (1964) (Am. Math. Soc. Trans. Ser. 2, 65, 139)
- R. Friedberg, T. D. Lee, and A. Sirlin, Phys. Rev. D 13, 2739 (1976)
- L. F. Abbott, J. S. Kang, and H. J. Schnitzer, Phys. Rev. D 13, 2212 (1976) M. Kobayashi and T. Kugo, Prog. Theor. Phys. 54, 1537 (1975) R. Haymaker, Phys. Rev. D 13, 968 (1975) L. Dolan and R. Jackiw, ibid. 9, 3320 (1974) H. J. Schnitzer, ibid. 10, 1800 (1974) ibid.10, 2042 (1974) S. Coleman, R. Jackiw, and H. D. Politzer, ibid. 10, 2491 (1974)
- H. J. Schnitzer, Nucl. Phys. B109, 297 (1976)
- R. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966)
- R. Newton, in Scattering Theory in Mathematical Physics, edited by J. A. Lavita and J.-P. Marchand (Reidel, Dordrecht, Holland, 1974)
- V. De Alfaro and T. Regge, Potential Scattering (North-Holland, Amsterdam, 1965)