4 research outputs found
-Deformation of Poincar\'e Superalgebra with Classical Lorentz Subalgebra and its Graded Bicrossproduct Structure
The -deformed Poincar{\'e} superalgebra written in Hopf
superalgebra form is transformed to the basis with classical Lorentz subalgebra
generators. We show that in such a basis the -deformed Poincare
superalgebra can be written as graded bicrossproduct. We show that the
-deformed superalgebra acts covariantly on -deformed
chiral superspace.Comment: 13 pages, late
Doubly Special Relativity and de Sitter space
In this paper we recall the construction of Doubly Special Relativity (DSR)
as a theory with energy-momentum space being the four dimensional de Sitter
space. Then the bases of the DSR theory can be understood as different
coordinate systems on this space. We investigate the emerging geometrical
picture of Doubly Special Relativity by presenting the basis independent
features of DSR that include the non-commutative structure of space-time and
the phase space algebra. Next we investigate the relation between our geometric
formulation and the one based on quantum -deformations of the
Poincar\'e algebra. Finally we re-derive the five-dimensional differential
calculus using the geometric method, and use it to write down the deformed
Klein-Gordon equation and to analyze its plane wave solutions.Comment: 26 pages, one formula (67) corrected; some remarks adde