In this review article we discuss some of the applications of noncommutative geometry in
physics that are of recent interest, such as noncommutative many-body systems …

We define a new homotopy algebraic structure, that we call a braided L_ ∞ L∞-algebra,
and use it to systematically construct a new class of noncommutative field theories, that we …

We study the possibility of obtaining noncommutative gravity dynamics from string theory in
the Seiberg–Witten limit. We find that the resulting low-energy theory contains more …

A bstract We consider gauge theories on Poisson manifolds emerging as semiclassical
approximations of noncommutative spacetime with Lie algebra type noncommutativity. We …

We present a noncommutative extension of Einstein-Hilbert gravity in the context of twist-
deformed space-time, with a⋆-product associated to a quite general triangular Drinfeld twist …

A bstract The Poisson gauge algebra is a semi-classical limit of complete non-commutative
gauge algebra. In the present work we formulate the Poisson gauge theory which is a …

A bstract We propose a field theoretical model defined on non-commutative space-time with
non-constant non-commutativity parameter Θ (x), which satisfies two main requirements: it is …

These are lecture notes for an introductory course on noncommutative field and gauge
theory. We begin by reviewing quantum mechanics as the prototypical noncommutative …

The problem of the consistent definition of gauge theories living on the non-commutative
(NC) spaces with a non-constant NC parameter Θ (x) Θ (x) is discussed. Working in the L …

We present a comparison of the noncommutative field theories built using two different star
products: Moyal and Wick-Voros (or normally ordered). For the latter we discuss both the …