UV dimensional reduction to two from group valued momenta

摘要

We describe a new model of deformed relativistic kinematics based on the group manifold U ( 1 ) × S U ( 2 ) as a four-momentum space. We discuss the action of the Lorentz group on such space and illustrate the deformed composition law for the group-valued momenta. Due to the geometric structure of the group, the deformed kinematics is governed by two energy scales λ and κ . A relevant feature of the model is that it exhibits a running spectral dimension d s with the characteristic short distance reduction to d s = 2 found in most quantum gravity scenarios.