A New “Null-Plane” Quantum Poincaré Algebra
نویسنده
چکیده
A new quantum deformation, which we call null-plane, of the (3+1) Poincaré algebra is obtained. The algebraic properties of the classical null-plane description are generalized to this quantum deformation. In particular, the classical isotopy subalgebra of the null-plane is deformed into a Hopf subalgebra, and deformed spin operators having classical commutation rules can be defined. Quantum Hamiltonian, mass and position operators are studied, and the null-plane evolution is expressed in terms of a deformed Schrödinger equation.
منابع مشابه
Non-standard quantum (1+1) Poincaré group: a T–matrix approach
The Hopf algebra dual form for the non–standard uniparametric deformation of the (1+1) Poincaré algebra iso(1, 1) is deduced. In this framework, the quantum coordinates that generate Funw(ISO(1, 1)) define an infinite dimensional Lie algebra. A change in the basis of the dual form is obtained in order to compare this deformation to the standard one. Finally, a non– standard quantum Heisenberg g...
متن کاملNon-standard quantum so(2,2) and beyond
A new “non-standard” quantization of the universal enveloping algebra of the split (natural) real form so(2, 2) of D2 is presented. Some (classical) graded contractions of so(2, 2) associated to a Z2 × Z2 grading are studied, and the automorphisms defining this grading are generalized to the quantum case, thus providing quantum contractions of this algebra. This produces a new family of “non-st...
متن کاملNon-standard quantum so(3, 2) and its contractions
A full (triangular) quantum deformation of so(3, 2) is presented by considering this algebra as the conformal algebra of the 2+1 dimensional Minkowskian spacetime. Non-relativistic contractions are analysed and used to obtain quantum Hopf structures for the conformal algebras of the 2+1 Galilean and Carroll spacetimes. Relations between the latter and the null-plane quantum Poincaré algebra are...
متن کاملA new ‘doubly special relativity’ theory from a quantum Weyl–Poincaré algebra
A ‘mass-like’ quantum Weyl–Poincaré 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 ...
متن کاملThree Dimensional Quantum Geometry and Deformed Poincaré Symmetry
We study a three dimensional non-commutative space emerging in the context of three dimensional Euclidean quantum gravity. Our starting point is the assumption that the isometry group is deformed to the Drinfeld double D(SU(2)) . We generalize to the deformed case the construction of E3 as the quotient of its isometry group ISU(2) by SU(2) . We show that the algebra of functions on E3 becomes t...
متن کامل