A Lagrangian for Dsr Particle and the Role of Noncommutativity
نویسنده
چکیده
In this paper we have constructed a coordinate space (or geometric) Lagrangian for a point particle that satisfies the exact Doubly Special Relativity (DSR) dispersion relation in the Magueijo-Smolin framework. Next we demonstrate how a Non-Commutative phase space is needed to maintain Lorentz invariance for the DSR dispersion relation. Lastly we address the very important issue of velocity of this DSR particle. Exploiting the above Non-commutative phase space algebra in a Hamiltonian framework, we show that the speed of massless particles is c and for massive particles the speed saturates at c when the particle energy reaches the maximum value κ, the Planck mass.
منابع مشابه
he p - th ] 1 8 A ug 2 00 7 DSR and Canonical Transformations : A Comment on a “ A Lagrangian for DSR particle and the role of noncommutativity ”
The aim of this comment is to call to the attention of DSR readers a basic fact. The introduction of noncommutative structures in problems like the one addressed in [1] is not necessary for the understanding of DSR physics. It can be described just as the relativistic free particle problem in a different parametrization. An important task of mathematical physics is to prove that a given mathema...
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