An Unfolded Quantization for Twisted Hopf Algebras

Abstract

In this talk I discuss a recently developed "Unfolded Quantization Framework". It allows to introduce a Hamiltonian Second Quantization based on a Hopf algebra endowed with a coproduct satisfying, for the Hamiltonian, the physical requirement of being a primitive element. The scheme can be applied to theories deformed via a Drinfeld twist. I discuss in particular two cases: the abelian twist deformation of a rotationally invariant nonrelativistic Quantum Mechanics (the twist induces a standard noncommutativity) and the Jordanian twist of the harmonic oscillator. In the latter case the twist induces a Snyder non-commutativity for the space-coordinates, with a pseudo-Hermitian deformed Hamiltonian. The "Unfolded Quantization Framework" unambiguously fixes the non-additive effective interactions in the multi-particle sector of the deformed quantum theory. The statistics of the particles is preserved even in the presence of a deformation.

9 pages. Talk given at QTS7 (7th Int. Conf. on Quantum Theory and Symmetries, Prague, August 2011)

References in corpus (5)

• Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
• Wigner Oscillators, Twisted Hopf Algebras and Second Quantization
• Twist Deformation of Rotationally Invariant Quantum Mechanics
• Lectures on Hopf Algebras, Quantum Groups and Twists
• Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation