|Author||Deshpande, Nilendra G.|
|Source||United States Department of Energy Office of Scientific and Technical Information|
|Publisher||American Physical Society (APS)|
|Subject Keyword||Physics (Theoretical)-Quantum Field Theories ♦ ZACHARIASEN MODEL- RENORMALIZATION ♦ COUPLING CONSTANTS ♦ N-D METHOD ♦ PROPAGATOR ♦ QUANTUM FIELD THEORY ♦ VERTEX FUNCTIONS|
|Abstract||The exactly soluble relativistic-model field theory proposed by Zachariasen is studied. The more general model with Yukawa and Fermi couplings is considered. The model thus admits a nontrivial vertex function as well as a propagator. Conventional renormalization is reviewed, and then renormalization is carried out at an arbitrary spacelike momentum. The equivalence of the two procedures is demonstrated. By setting up the equations for the Yakawa and Fermi constants at Euclidean momenta in terms of the one-mass-shell couplings, the asymptotic limit is taken. It is shown that both the Yukawa and Fermi constants vanish in the limit, thus providing an example of an asymptotically free theory. Since the model has an S-matrix formulation, the connection is seen between the renormalization-group method and the point of subtraction in the N/D technique. The Gell-Mann-Low equations for the coupling are set up and solved, exactly, again verifying the asymptotic freedom.|
|Learning Resource Type||Article|
|Publisher Department||Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403|
|Publisher Place||United States|
|Journal||Physical Review. D, Particles Fields|
|Organization||Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403|
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