A New Null-Plane Quantum Poincare Algebra

Abstract

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.

13 pages, LaTeX

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• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• 4D Quantum Affine Algebras and Space--Time q-Symmetries
• Non-standard quantum so(2,2) and beyond

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