Strong and electroweak interactions and their unification with non-commutative space-time

Quantum field theories based on non-commutative space-time (NCQFT) have been extensively studied recently. However no NCQFT model which can uniquely describe the strong and electroweak interactions has been constructed. This prevents one to make a consistent and systematic study of noncommutative space-time. In this work we construct a NCQFT model based on the trinification gauge group SU(3)(c) x SU(3)(L) x SU(3)(R). A unique feature of this model, that all matter fields (fermions and Higgs bosons) are assigned to (anti-) fundamental representations of the factor SU(3) groups, allows us to construct a NCQFT model for strong and electroweak interactions and their unification without ambiguities. This model provides an example which allows one to make a consistent and systematic study of non-commutative space-time phenomenology. We also comment on some related issues regarding extensions to E-6 and U(3)(c) x U(3)(L) x U(3)(R) models.