Strong, Electroweak Interactions and Their Unification with Noncommutative Space-time

Quantum field theories based on noncommutative 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 consistent and systematic study of noncommutative space-time. In this work we construct a NCQFT model based on the trinification gauge group $SU(3)_C\times SU(3)_L\times SU(3)_R$. A unique feature of this model, that all matter fields (fermions and Higgses) 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 consistent and systematic study of noncommutative space-time phenomenology. We also comment on some related issues regarding extensions to $E_6$ and $U(3)_C\times U(3)_L\times U(3)_R$ models.Comment: 12 pages, Revtex, no figures. Version to be published in ERJ

Dispersion Relations Explaining OPERA Data From Deformed Lorentz Transformation

OPERA collaboration has reported evidence of superluminal phenomenon for neutrinos. One of the possible ways to explain the superluminality is to have Lorentz symmetry violated. It has been shown that dispersion relations put forwards has the problem of physics laws vary in different inertial frames leading to conflicting results on Cherenkov-like radiation, pion decay and high energy neutrino cosmic ray. For theories with deformed Lorentz symmetry, by modifying conservation laws corresponding to energy and momentum in the usual Lorentz invariant theory, it is possible to have superluminal effect and at the same time avoid to have conflicts encountered in Lorentz violating theories. We study dispersion relations from deformed Lorentz symmetry. We find that it is possible to have dispersion relations which can be consistent with data on neutrinos. We show that once the superluminality $\delta v$ as a function of energy is known the corresponding dispersion relation in the deformed Lorentz symmetry can be determined.Comment: 8 pages, 2 figures. Several typos corrected and some references adde