Heisenberg Doubles for Snyder-Type Models
Stjepan Meljanac, Anna Pachoł
Abstract
A Snyder model generated by the noncommutative coordinates and Lorentz generators closes a Lie algebra. The application of the Heisenberg double construction is investigated for the Snyder coordinates and momenta generators. This leads to the phase space of the Snyder model. Further, the extended Snyder algebra is constructed by using the Lorentz algebra, in one dimension higher. The dual pair of extended Snyder algebra and extended Snyder group is then formulated. Two Heisenberg doubles are considered, one with the conjugate tensorial momenta and another with the Lorentz matrices. Explicit formulae for all Heisenberg doubles are given.
Topics & Concepts
Noncommutative geometryPhysicsLorentz transformationHeisenberg groupLie algebraDimension (graph theory)Mathematical physicsHeisenberg pictureNoncommutative algebraic geometryHeisenberg modelLorentz covarianceLorentz groupPhase spaceVelocity-addition formulaAlgebra over a fieldLie groupSpace (punctuation)Quantum mechanicsMathematicsBispinorNoncommutative quantum field theoryGroup (periodic table)Quantum differential calculusLorentz spaceNoncommutative and Quantum Gravity TheoriesBlack Holes and Theoretical PhysicsQuantum and Classical Electrodynamics