Callan-Symanzik equation and asymptotic freedom in the Marr-Shimamoto model
- 2599 Canadian Goose Circle, Henderson, Nevada 89052 (United States) and Department of Physics, University of Vermont, Burlington, Vermont 05401 (United States)
The exactly soluble nonrelativistic Marr-Shimamoto model was introduced in 1964 as an example of the Lee model with a propagator and a nontrivial vertex function. An exactly soluble relativistic version of this model, known as the Zachariasen model, has been found to be asymptotically free in terms of coupling constant renormalization at an arbitrary spacelike momentum and on the basis of exact solutions of the Gell-Mann-Low equations. This is accomplished with conventional cut-off regularization by setting up the Yukawa and Fermi coupling constants at Euclidean momenta in terms of on mass-shell couplings and then taking the asymptotic limit. In view of this background, it may be expected that an investigation of the nonrelativistic Marr-Shimamoto theory may also exhibit asymptotic freedom in view of its manifest mathematical similarity to that of the Zachariasen model. To prove this point, the present paper prefers to examine asymptotic freedom in the nonrelativistic Marr-Shimamoto theory using the powerful concepts of the renormalization group and the Callan-Symanzik equation, in conjunction with the specificity of dimensional regularization and on-shell renormalization. This approach is based on calculations of the Callan-Symanzik coefficients and determinations of the effective coupling constants. It is shown that the Marr-Shimamoto theory is asymptotically free for dimensions D<3 and for values of D>3 occurring in periodic intervals over the range of 0<D<27 of particular interest. This differs from the original Lee model which has been shown by several authors, using these same concepts, to be asymptotically free only for D<4.
- OSTI ID:
- 21335954
- Journal Information:
- Journal of Mathematical Physics, Vol. 51, Issue 5; Other Information: DOI: 10.1063/1.3431035; (c) 2010 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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