Noncommutative Spacetimes
Symmetries in Noncommutative Geometry and Field Theory
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Open AccessNoncommutative gauge and gravity theories and geometric Seiberg–Witten map
We give a pedagogical account of noncommutative gauge and gravity theories, where the exterior product between forms is deformed into a $$\sta...
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Article
Open AccessBraided Hopf Algebras and Gauge Transformations II: \(*\) -Structures and Examples
We consider noncommutative principal bundles which are equivariant under a triangular Hopf algebra. We present explicit examples of infinite dimensional braided Lie and Hopf algebras of infinitesimal gauge tra...
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Chapter and Conference Paper
Levi-Civita Connections on Braided Algebras
A braided symmetric algebra carries a representation of a triangular Hopf algebra. Its noncommutativity is captured by the universal R-matrix. Its differential geometry is canonically constructed from these data....
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Article
On Curvature and Torsion in Courant Algebroids
We study the graded geometric point of view of curvature and torsion of Q-manifolds (differential graded manifolds). In particular, we get a natural graded geometric definition of Courant algebroid curvature and ...
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Article
Open AccessQuantum Principal Bundles on Projective Bases
The purpose of this paper is to propose a sheaf theoretic approach to the theory of quantum principal bundles over non affine bases. We study noncommutative principal bundles corresponding to
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Article
Global Seiberg–Witten Maps for U(n)-Bundles on Tori and T-duality
Seiberg–Witten maps are a well-established method to locally construct noncommutative gauge theories starting from commutative gauge theories. We revisit and classify the ambiguities and the freedom in the def...
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Article
Open AccessNonassociative differential geometry and gravity with non-geometric fluxes
We systematically develop the metric aspects of nonassociative differential geometry tailored to the parabolic phase space model of constant locally non-geometric closed string vacua, and use it to construct p...
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Article
Open AccessObservables and dispersion relations in κ-Minkowski spacetime
We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical...
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Article
Noncommutative Principal Bundles Through Twist Deformation
We construct noncommutative principal bundles deforming principal bundles with a Drinfeld twist (2-cocycle). If the twist is associated with the structure group then we have a deformation of the fibers. If the...
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Article
Open AccessNoncommutative Chern-Simons gauge and gravity theories and their geometric Seiberg-Witten map
We use a geometric generalization of the Seiberg-Witten map between noncommutative and commutative gauge theories to find the expansion of noncommutative Chern-Simons (CS) theory in any odd dimension D and at fir...
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Chapter and Conference Paper
Extended Gravity from Noncommutativity
We present a first order theory of gravity (vierbein formulation) on noncommutative spacetime. The first order formalism allows to couple the theory to fermions. This NC action is then reinterpreted (using the...
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Chapter and Conference Paper
Constitutive Relations, Off Shell Duality Rotations and the Hypergeometric Form of Born-Infeld Theory
We review equivalent formulations of nonlinear and higher derivatives theories of electromagnetism exhibiting electric-magnetic duality rotations symmetry. We study in particular on shell and off shell formula...
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Article
Open AccessConstitutive relations and Schrödinger’s formulation of nonlinear electromagnetic theories
We present a systematic study of nonlinear and higher derivatives extensions of electromagnetism. We clarify when action functionals S[F] can be explicitly obtained from arbitrary (not necessarily self-dual) nonl...
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Article
Noncommutative gauge fields coupled to noncommutative gravity
We present a noncommutative (NC) version of the action for vielbein gravity coupled to gauge fields. Noncommutativity is encoded in a twisted ...
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Article
Extended gravity theories from dynamical noncommutativity
In this paper we couple noncommutative vielbein gravity to scalar fields. Noncommutativity is encoded in a \(\star \)
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Article
Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map
We use the Seiberg-Witten map (SW map) to expand noncommutative gravity coupled to fermions in terms of ordinary commuting fields. The action is invariant under general coordinate transformations and local Lor...
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Article
Noncommutative quantum field theory and gravity
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Book
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Chapter
The Noncommutative Geometry of Julius Wess
Julius Wess first work on noncommutative geometry dates June 1989. Since then he gradually became more and more interested and involved in this research field. We would like to describe briefly his interests, ...
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Chapter
Noncommutative Symmetries and Gravity
Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star multiplied. Consistently, spacetime diffeomorphisms are twisted into noncommutative dif...
