Related papers: Non-anti-commutative deformation of complex geomet…
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible…
It is outlined how deformations of field theoretical rigid symmetries can be constructed and classified by cohomological means in the extended antifield formalism. Special attention is devoted to deformations referring only to a subset of…
Classical differential geometry can be encoded in spectral data, such as Connes' spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in terms of supersymmetric spectral data. This leads…
This talk is an introduction to ideas of non-commutative geometry and star products. We will discuss consequences for physics in two different settings: quantum field theories and astrophysics. In case of quantum field theory, we will…
We propose the definition of (twisted) generalized hyperkaehler geometry and its relation to supersymmetric non-linear sigma models. We also construct the corresponding twistor space.
In a previous paper we developed a formalism to construct (potentially) supersymmetric theories in the context of noncommutative geometry. We apply this formalism to explore the existence of a noncommutative version of the minimal…
Noncommutative geometry has seen remarkable applications for high energy physics, viz. the geometrical interpretation of the Standard Model. The question whether it also allows for supersymmetric theories has so far not been answered in a…
We propose a type of non-anticommutative superspace, with the interesting property of relating to Lee-Wick type of higher derivatives theories, which are known for their interesting properties, and have lead to proposals of…
In this paper the model considered by Arkani-Hamed, Cohen and Georgi in the context of (de)constructing dimensions has been studied by making use of non-commutative geometry. The non-commutative geometry provides a natural framework to…
We review some applications of noncommutative geometry to the study of transverse geometry of Riemannian foliations and discuss open problems.
Non(anti)commutativity in an open free superstring and also one moving in a background anti-symmetric tensor field is investigated. In both cases, the non(anti)commutativity is shown to be a direct consequence of the non-trivial boundary…
Supersymmetric nonlinear sigma models are formulated as gauge theories. Auxiliary chiral superfields are introduced to impose supersymmetric constraints of F-type. Target manifolds defined by F-type constraints are always non-compact. In…
We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.
We review some aspects of the implementation of spacetime symmetries in noncommutative field theories, emphasizing their origin in string theory and how they may be used to construct theories of gravitation. The geometry of canonical…
Supersymmetric field theories on noncommutative spaces are constructed. We present two different representations of noncommutative space, but we can obtain supersymmetry algebla and supersymmetric Yang-Mills action independent of its…
Based on an argument for the noncommutativity of momenta in noncommutative directions, we arrive at a generalization of the ${\cal N}=1$ super $E^2$ algebra associated to the deformation of translations in a noncommutative Euclidean plane.…
Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie…
This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral…
We consider a deformation of N=1 four dimensional Minkowski superspace where odd coordinates $\theta^{\alpha}$ do not anticommute. We define supersymmetric and associative star product and show how the remaining (anti)commutation relations…
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. A brief survey of main parts of noncommutative geometry with historical remarks, bibliography and a list of exercises…