| Summary: | 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. === Science, Faculty of === Physics and Astronomy, Department of === Graduate
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