# A Star Product for Differential Forms on Symplectic Manifolds

@article{Tagliaferro2008ASP, title={A Star Product for Differential Forms on Symplectic Manifolds}, author={Anthony Tagliaferro}, journal={arXiv: High Energy Physics - Theory}, year={2008} }

We present a star product between differential forms to second order in the deformation parameter $\hbar$. The star product obtained is consistent with a graded differential Poisson algebra structure on a symplectic manifold. The form of the graded differential Poisson algebra requires the introduction of a connection with torsion on the manifold, and places various constraints upon it. The star product is given to second order in $\hbar^2$.

## 15 Citations

### COVARIANT STAR PRODUCT ON SYMPLECTIC AND POISSON SPACE–TIME MANIFOLDS

- Mathematics
- 2010

A covariant Poisson bracket and an associated covariant star product in the sense of deformation quantization are defined on the algebra of tensor-valued differential forms on a symplectic manifold,…

### Noncommutative gauge theory using a covariant star product defined between Lie-valued differential forms

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We develop an internal gauge theory using a covariant star product. The space-time is a symplectic manifold endowed only with torsion but no curvature. It is shown that, in order to assure the…

### Gauge field theories with covariant star-product

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- 2009

A noncommutative gauge theory is developed using a covariant star-product between differential forms defined on a symplectic manifold, considered as the space-time. It is proven that the field…

### Noncommutative differential forms on the kappa-deformed space

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We construct a differential algebra of forms on the kappa-deformed space. For a given realization of noncommutative coordinates as formal power series in the Weyl algebra we find an infinite family…

### Diffeomorphism covariant star products and noncommutative gravity

- Mathematics
- 2009

The use of a diffeomorphism covariant star product enables us to construct diffeomorphism invariant gravities on noncommutative symplectic manifolds without twisting the symmetries. As an example, we…

### 4D Higher Spin Gravity with Dynamical Two-Form as a Frobenius-Chern-Simons Gauge Theory

- Mathematics
- 2015

We provide an off-shell formulation of four-dimensional higher spin gravity based on a covariant Hamiltonian action on an open nine-dimensional Poisson manifold whose boundary consists of the direct…

### 2D sigma models and differential Poisson algebras

- Mathematics
- 2015

A bstractWe construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and…

### Integrable Hopf twists, marginal deformations and generalised geometry

- Physics
- 2016

The Leigh-Strassler family of N=1 marginal deformations of the N=4 SYM theory admits a Hopf algebra symmetry which is a quantum group deformation of the SU(3) part of the R-symmetry of the Ncal=4…

### 4D higher spin black holes with nonlinear scalar fluctuations

- Physics
- 2017

A bstractWe construct an infinite-dimensional space of solutions to Vasiliev’s equations in four dimensions that are asymptotic to AdS spacetime and superpose massless scalar particle modes over…

### Quantum Space-Time and Noncommutative Gauge Field Theories

- Physics
- 2009

The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One…

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