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An Unfolded Quantization for Twisted Hopf Algebras
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An Unfolded Quantization for Twisted Hopf Algebras
An Unfolded Quantization for Twisted Hopf Algebras
Journal Article

An Unfolded Quantization for Twisted Hopf Algebras

2012
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Overview
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 Drinfel'd 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.