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**Physics Note****Published**

# **An Unfolded Quantization for Twisted Hopf Algebras**

**F. Toppan**

12/07/2011

[**Download PDF **0.3 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb9db/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=An%20Unfolded%20Quantization%20for%20Twisted%20Hopf%20Algebras)

## **Publication details**

<dl>

<dt>Authors</dt>
<dd>F. Toppan</dd>

<dt>Type</dt>
<dd>Physics Note</dd>

<dt>Status</dt>
<dd>Published</dd>

<dt>Publication date</dt>
<dd>07/12/2011</dd>

<dt>Description</dt>
<dd>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.\par 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.</dd>

<dt>Year</dt>
<dd>2011</dd>

<dt>Number</dt>
<dd>CBPF-NF-005/11</dd>

<dt>Linked to a thesis</dt>
<dd>No</dd>

<dt>Linked to a grant</dt>
<dd>No</dd>

</dl>

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