N G DESHPANDE

Institute of Theoretical Science and Department of Physics, University of Oregon, Eugene, OR 97403-5203, USA

Email: desh@oregon.uoregon.edu

Abstract. Construction of quantum field theory based on operators that are functions of non-commutative space-time operators is reviewed. Examples of $\phi^4$ theory and QED are then discussed. Problems of extending the theories to $SU(N)$ gauge theories and arbitrary charges in QED are considered. Construction of standard model on non-commutative space is then briefly discussed. The phenomenological implications are then considered. Limits on non-commutativity from atomic physics as well as accelerator experiments are presented.

Keywords. Non-commutative geometry; non-commutative gause theory.

PACS Nos 11.10.Nx; 11.30.Cp; 11.15.-q