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The standard model on non-commutative space-time
Abstract. We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter $\theta^{\mu \nu}$. No new particles are introduced; the structure groupExpand
Enveloping algebra-valued gauge transformations for non-abelian gauge groups on non-commutative spaces
Abstract. An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allowsExpand
Noncommutative Yang-Mills from equivalence of star products
Abstract. It is shown that the transformation between ordinary and noncommutative Yang-Mills theory as formulated by Seiberg and Witten is due to the equivalence of certain star products on theExpand
Construction of non-Abelian gauge theories on noncommutative spaces
Abstract. We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation.Expand
Noncommutative Line Bundle and Morita Equivalence
Global properties of Abelian noncommutative gauge theories based on ⋆-products which are deformation quantizations of arbitrary Poisson structures are studied. The consistency condition for finiteExpand
NonAbelian noncommutative gauge theory via noncommutative extra dimensions
The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arises in string theory with backgroundExpand
Classical Yang–Baxter equations and quantum integrable systems
Quantum integrable models associated with nondegenerate solutions of classical Yang–Baxter equations related to the simple Lie algebras are investigated. These models are diagonalized for rationalExpand
Semistrict higher gauge theory
A bstractWe develop semistrict higher gauge theory from first principles. In particular, we describe the differential Deligne cohomology underlying semistrict principal 2-bundles with connectiveExpand
Nonabelian Bundle Gerbes, Their Differential Geometry and Gauge Theory
Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studiedExpand
L∞‐Algebras of Classical Field Theories and the Batalin–Vilkovisky Formalism
We review in detail the Batalin-Vilkovisky formalism for Lagrangian field theories and its mathematical foundations with an emphasis on higher algebraic structures and classical field theories. InExpand