# Twisting all the way: From classical mechanics to quantum fields

@article{Aschieri2008TwistingAT, title={Twisting all the way: From classical mechanics to quantum fields}, author={Paolo Aschieri and Fedele Lizzi and Patrizia Vitale}, journal={Physical Review D}, year={2008}, volume={77}, pages={025037} }

We discuss the effects that a noncommutative geometry induced by a Drinfeld twist has on physical theories. We systematically deform all products and symmetries of the theory. We discuss noncommutative classical mechanics, in particular its deformed Poisson bracket and hence time evolution and symmetries. The twisting is then extended to classical fields, and then to the main interest of this work: quantum fields. This leads to a geometric formulation of quantization on noncommutative space…

## 87 Citations

Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes

- Mathematics
- 2009

In this article we study the quantization of a free real scalar field on a class of noncommutative manifolds, obtained via formal deformation quantization using triangular Drinfel’d twists. We…

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We re-examine various issues surrounding the definition of twisted quantum field theories on flat noncommutative spaces. We propose an interpretation based on nonlocal commutative field redefinitions…

Star product geometries

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Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes

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As a preparation for a mathematically consistent study of the physics of symmetric spacetimes in a noncommutative setting, we study symmetry reductions in deformed gravity. We focus on deformations…

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In a minimalistic view, the use of noncommutative coordinates can be seen just as a way to better express non-local interactions of a special kind: 1-particle solutions (wavefunctions) of the…

Wedge locality and asymptotic commutativity

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- 2014

In this paper, we study twist deformed quantum field theories obtained by combining the Wightman axiomatic approach with the idea of spacetime noncommutativity. We prove that the deformed fields with…

Twisted statistics and the structure of Lie-deformed Minkowski spaces

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- 2017

We show that the realizations of noncommutative coordinates that are linear in the Lorentz generators form a closed Lie algebra under certain conditions. The star product and the coproduct for the…

Inequivalence of quantum field theories on noncommutative spacetimes: Moyal versus Wick-Voros planes

- Physics
- 2010

In this paper, we further develop the analysis started in an earlier paper on the inequivalence of certain quantum field theories on noncommutative spacetimes constructed using twisted fields. The…

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