Related papers: $L_\infty$-Bootstrap Approach to Non-Commutative G…
Non-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L$_\infty$ algebra, that governs not only the action of the symmetries but also…
The problem of the consistent definition of gauge theories living on the non-commutative (NC) spaces with a non-constant NC parameter $\Theta(x)$ is discussed. Working in the L$_\infty$ formalism we specify the undeformed theory, $3$d…
The Poisson gauge theory is a semi-classical limit of full non-commutative gauge theory. In this work we construct an L$_\infty^{full}$ algebra which governs both the action of gauge symmetries and the dynamics of the Poisson gauge theory.…
We propose a field theoretical model defined on non-commutative space-time with non-constant non-commutativity parameter $\Theta(x)$, which satisfies two main requirements: it is gauge invariant and reproduces in the commutative limit,…
This work is devoted to review the gauge embedding of either commutative and noncommutative (NC) theories using the symplectic formalism framework. To sum up the main features of the method, during the process of embedding, the…
In this work, we generalize the non-geometrical construction of gauge theories, due to S. Deser, to a noncommutative setting. We show that in a free theory, along with the usual local N\"{o}ther current, there is another conserved current,…
We study space-time symmetries in Non-Commutative (NC) gauge theory in the (constrained) Hamiltonian framework. The specific example of NC CP(1) model, posited in \cite{sg}, has been considered. Subtle features of Lorentz invariance…
We study the generalization of S-duality to non-commutative gauge theories. For rank one theories, we obtain the leading terms of the dual theory by Legendre transforming the Lagrangian of the non-commutative theory expressed in terms of a…
Starting from a standard noncommutative gauge theory and using the Seiberg-Witten map we propose a new version of a noncommutative gravity. We use consistent deformation theory starting from a free gauge action and gauging a killing…
We give a pedagogical introduction to $L_\infty$-algebras and their uses in organising the symmetries and dynamics of classical field theories, as well as of the conventional noncommutative gauge theories that arise as low-energy effective…
We review and develop the general properties of $L_\infty$ algebras focusing on the gauge structure of the associated field theories. Motivated by the $L_\infty$ homotopy Lie algebra of closed string field theory and the work of Roytenberg…
We construct a family of four-dimensional noncommutative deformations of $U(1)$ gauge theory following a general scheme, recently proposed in JHEP 08 (2020) 041 for a class of coordinate-dependent noncommutative algebras. This class…
Lie-Poisson gauge formalism provides a semiclassical description of noncommutative $U(1)$ gauge theory with Lie algebra type noncommutativity. Using the Dirac approach to constrained Hamiltonian systems, we focus on a class of Lie-Poisson…
The quantization of spontaneously broken gauge theories in noncommutative geometry(NCG) has been sought for some time, because quantization is crucial for making the NCG approach a reliable and physically acceptable theory. Lee, Hwang and…
The semiclassical limit of full non-commutative gauge theory is known as Poisson gauge theory. In this work we revise the construction of Poisson gauge theory paying attention to the geometric meaning of the structures involved and advance…
We explicitly construct an L$_\infty$ algebra that defines U$_{\star}(1)$ gauge transformations on a space with an arbitrary non-commutative and even non-associative star product. Matter fields are naturally incorporated in this scheme as…
In this thesis noncommutative gauge theory is extended beyond the canonical case, i.e. to structures where the commutator no longer is a constant. In the first part noncommutative spaces created by star-products are studied. We are able to…
We summarise recent perspectives on symmetries of noncommutative field theories based on homotopy algebras. We show how these viewpoints naturally lead to a new class of noncommutative field theories which possess braided gauge symmetries,…
We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory…
The aim of this paper is to extend existence results for the Coulomb gauge from standard gauge theory to a non-associative setting. Non-associative gauge theory is based on smooth loops, which are the non-associative analogs of Lie groups.…