Classical Velocity in kappa-deformed Poincare Algebra and a Maximum Acceleration

Abstract

We study the commutators of the kappa-deformed Poincare Algebra (kappaPA) in an arbitrary basis. It is known that the two recently studied doubly special relativity theories correspond to different choices of kappaPA bases. We present another such example. We consider the classical limit of kappaPA and calculate particle velocity in an arbitrary basis. It has standard properties and its expression takes a simple form in terms of the variables in the Snyder basis. We then study the particle trajectory explicitly for the case of a constant force. Assuming that the spacetime continuum, velocity, acceleration, etc. can be defined only at length scales greater than x_{min} ne 0, we show that the acceleration has a finite maximum.