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The quartic interaction in the large-N limit of quantum field theory on a noncummutative space DeBoer, Philip Albert

Abstract

With a view to understanding generic properties of quantum field theories defined on spaces with noncommuting spatial coordinates (termed noncommutative quantum field theories), two simple models are considered. The first model is a theory of bosonic vector fields having an O(N)-symmetric quartic interaction. The second model is the fermionic counterpart of the bosonic theory, and is known as the Gross-Neveu model. In both cases the study is conducted in the simplifying large-TV limit. Unlike in the commutative case, the noncommutative theory gives rise to two inequivalent quartic interactions of the form (Φ²)² and (Φ[sup i] Φ[sup j])². The latter interaction is difficult to work with, but significant progress is made for the theories containing only the former interaction.

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