Introduction to Doubly Special Relativity

We construct a Dirac equation that is consistent with one of the recently-proposed schemes for a "doubly-special relativity", a relativity with both an observer-independent velocity scale (still naturally identified with the speed-of-light constant) and an observer-independent length/momentum scale (possibly given by the Planck length/momentum). We find that the introduction of the second observer-independent scale only induces a mild deformation of the structure of Dirac spi...

We propose new noncommutative (NC) models of quantum phase spaces, containing a pair of $\kappa$-deformed Poincar\'e algebras, with two independent $\kappa$ and $\tilde{\kappa}$-deformations in space-time and fourmomenta sectors. The first quantum phase space can be obtained by contractions $M,R\to \infty$ of recently introduced doubly $\kappa$-deformed $(\kappa,\tilde{\kappa})$-Yang models, with the parameters $M,R$ describing inverse space-time and fourmomenta curvatures an...

We propose a new interpretation of doubly special relativity (DSR) based on the distinction between the momentum and the translation generators in its phase space realization. We also argue that the implementation of DSR theories does not necessarily require a deformation of the Lorentz symmetry, but only of the translation invariance.

A mass-like quantum Weyl-Poincare algebra is proposed to describe, after the identification of the deformation parameter with the Planck length, a new relativistic theory with two observer-independent scales (or DSR theory). Deformed momentum representation, finite boost transformations, range of rapidity, energy and momentum, as well as position and velocity operators are explicitly studied and compared with those of previous DSR theories based on kappa-Poincare algebra. The...

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 Ha...

We study the \k{appa}-Poincare and the Magueijo-Smolin (MS) DSR in the context of the relative locality theory. This theory assigns connection, torsion and curvature to momentum space of every modified theory beyond special relativity. We obtain these quantities for the \k{appa}-Poincare and the MS DSR in all order of the Planck length, at the every point of the momentum space. The connection for the \k{appa}-Poincare theory and the MS DSR can be non-zero. The torsion for the...

Recently Amelino--Camelia proposed a ``Doubly Special Relativity'' theory with two observer independent scales (of speed and mass) that could replace the standard Special Relativity at energies close to the Planck scale. Such a theory might be a starting point in construction of quantum theory of space-time. In this paper we investigate the quantum and statistical mechanical consequences of such a proposal. We construct the generalized Newton--Wigner operator and find relatio...

We show that depending on the direction of deformation of $\kappa$-Poincar\'e algebra (time-like, space-like, or light-like) the associated phase spaces of single particle in Doubly Special Relativity theories have the energy-momentum spaces of the form of de Sitter, anti-de Sitter, and flat space, respectively.

Following our earlier work \cite{sunandan1, sunandan2}, we derive noncommuting phase-space structures which are combinations of both the $\kappa$-Minkowski and Snyder algebra by exploiting the reparametrisation symmetry of the recently proposed Lagrangian for a point particle \cite{subir} satisfying the exact Doubly Special Relativity dispersion relation in the Magueijo-Smolin framework.

We develop a new description of the much-studied $\kappa$-Minkowski noncommutative spacetime, centered on representing on a single Hilbert space not only the $\kappa$-Minkowski coordinates, but also the associated differential calculus and the $\kappa$-Poincar\'e symmetry generators. In this "pregeometric" representation the relevant operators act on the kinematical Hilbert space of the covariant formulation of quantum mechanics, which we argue is the natural framework for ...