The quartic interaction in the large-N limit of quantum field theory on a noncummutative space
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...
| Main Author: | |
|---|---|
| Language: | English |
| Published: |
2009
|
| Online Access: | http://hdl.handle.net/2429/11683 |
| 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. |
|---|