Abstract
The scalar interaction and the Fermi interaction are studied for space-time dimension between 2 and 4. An unconventional coupling-constant renormalization is used: () and , with and held fixed as the cutoff . The theories can be solved in two limits: (1) the limit where and are fields with components, and (2) the limit of small , as a power series in . Both theories exhibit scale invariance with anomalous dimensions in the zero-mass limit. For small , the fields , , and all have anomalous dimensions, except for the stress-energy tensor. These anomalous dimensions are calculated through order ; they are remarkably close to canonical except for . The interaction is studied only for large ; for small it generates a weakly interacting composite boson. Both the and theories as solved here reduce to trivial free-field theories for . This paper is motivated by previous work in classical statistical mechanics by Stanley (the limit) and by Fisher and Wilson (the expansion).
- Received 9 November 1972
DOI:https://doi.org/10.1103/PhysRevD.7.2911
©1973 American Physical Society