Random walk representations and four-fermion interactions

Journal Article · Tue Feb 15 04:00:00 EST 1994 · Annals of Physics (New York); (United States)

DOI:https://doi.org/10.1006/aphy.1994.1017· OSTI ID:6828359

Jaroszewicz, T ^[1]; Kurzepa, P S ^[2]

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1. Univ. of California, Los Angeles, CA (United States)
2. Los Alamos National Laboratory, NM (United States)

The authors develop a new, nonperturbative method of analysis of quantum field theories of interacting fermions. Their approach is based on the previously developed representation of fermion propagation in terms of smooth, directed random walks. This method generalizes Symanzik's polymer gas' description of bosonic quantum field. They derive and analyze the Hausdorff, recurrence, and intersection properties of directed random walks, and provide a complete description of fermion correlation functions in terms of intersection local times of these walks. They then consider the ([psi][psi])[sup 2] interaction both in the 1/N expansion and in the N [yields] O limit. They show that, if the fermion-fermion interaction is repulsive, the renormalized theory is free above two spacetime dimensions. Attractive interactions, however, may lead to the appearance of a propagating boson in the spectrum of the theory. In that case the resultant finite-range fermion-fermion interactions modify the upper critical dimension to four. 77 refs.

• OSTI ID: 6828359
• Journal Information: Annals of Physics (New York); (United States), Journal Name: Annals of Physics (New York); (United States) Vol. 230:1; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

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