An Unfolded Quantization for Twisted Hopf Algebras

TL;DR

This paper introduces the Unfolded Quantization Framework, enabling Hamiltonian second quantization for twisted Hopf algebras, preserving particle statistics and fixing multi-particle interactions in deformed quantum theories.

Contribution

It presents a novel quantization scheme applicable to Drinfeld twist deformations, clarifying multi-particle interactions and particle statistics preservation.

Findings

Applied to abelian twist deformation of nonrelativistic quantum mechanics

Analyzed Jordanian twist of the harmonic oscillator leading to Snyder non-commutativity

Framework unambiguously determines non-additive interactions in deformed theories

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.