Post #525768

For the #dailyPaperChallenge, I have read the #paperOfTheDay "Four-fermion interaction near four dimensions" from 1991. There are a few model systems that have been studied extensively in #quantumFieldTheory and wider theoretical #physics . Among them are the phi^4 theory (scalar field with quartic interaction) which can be treated perturbatively in 4-dimensional spacetime. The Gross-Neveu model (Fermions with quartic interaction) and nonlinear sigma model (scalars with non-monomial interaction) are renormalizable only in 2-dimensional spacetime. For each of them, a large-N expansion can be used as an alternative to a small-coupling expansion. The present paper, firstly, is a nice overview of the features of these various models. Secondly, it studies the possibility to have effective 4-fermion interactions in 4 dimensions. The Gross-Neveu model as such is not renormalizable there, but one can, essentially, couple it to a scalar field theory, which then effectively acts as a mediator to enable 4-fermion interactions. A similar mechanism is at play in the real world, in the standard model of particle physics. The difference is that the true mediators (the standard model gauge bosons) carry spin and charges and complicated interactions, whereas the present model uses a much simplified version of an intermediate particle. https://www.sciencedirect.com/science/article/pii/055032139190043W