Related papers: Trace extensions, determinant bundles, and gauge g…
We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincar\'e invariance. We determine the constraints…
We show how quiver representations and their invariant theory natu- rally arise in the study of some moduli spaces parametrizing bundles dened on an algebraic curve, and how they lead to ne results regarding the geometry of these spaces.
The Courant bracket defined originally on the sections of the vector bundle $TM \oplus T^*M \to M$ is extended to the direct sum of the 1-jet vector bundle and its dual. The extended bracket allows to interpret many structures encountered…
We study differential operators, whose coefficients define noncommutative algebras. As algebra of coefficients, we consider crossed products, corresponding to action of a discrete group on a smooth manifold. We give index formulas for…
We establish a Poincar\'e-Dulac theorem for sequences (G_n)_n of holomorphic contractions whose differentials d_0 G_n split regularly. The resonant relations determining the normal forms hold on the moduli of the exponential rates of…
This paper shows how the forms of gauge theory, Hamiltonian mechanics and quantum mechanics arise from a non-commutative framework for calculus and differential geometry. Discrete calculus is seen to fit into this pattern by reformulating…
Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz' approach to the present context. Representation theoretical properties of the differential calculi are investigated. Connections on quantum…
We give a brief overview of recent progress in understanding Bagger-Witten line bundles, which are bundles over moduli spaces of two-dimensional N=2 SCFTs whose existence is a consequence of the global U(1)_R symmetry of the theories. Our…
The appearance of noncommuting spatial coordinates is studied in quantum systems containing a magnetic monopole and under the influence of a radial potential. We derive expressions for the commutators of the coordinates that have been…
We study gauge theories based on abelian $p-$ forms on real compact hyperbolic manifolds. The tensor kernel trace formula and the spectral functions associated with free generalized gauge fields are analyzed.
We consider families of random non-unitary contraction operators defined as deformations of CMV matrices which appear naturally in the study of random quantum walks on trees or lattices. We establish several deterministic and almost sure…
We extend formulae which measure discrepancies for regularized traces on classical pseudodifferential operators to regularized trace cochains, regularized traces corresponding to 0-regularized trace cochains. This extension from 0-cochains…
The direct string computation of anomalous D-brane and orientifold plane couplings is extended to include the curvature of the normal bundle. The normalization of these terms is fixed unambiguously. New, non-anomalous gravitational…
The equivalence problem for linear differential operators of the second order, acting in vector bundles, is discussed. The field of rational invariants of symbols is described and connections, naturally accosiated with differential…
Using the method of Witten deformation, we express the basic index of a transversal Dirac operator over a Riemannian foliation as the sum of integers associated to the critical leaf closures of a given foliated bundle map.
The relational formalism based on geometrical clocks and Dirac observables in linearized canonical cosmological perturbation theory is used to introduce an efficient method to find evolution equations for gauge invariant variables. Our…
Symplectic spinors form an infinite-rank vector bundle. Dirac operators on this bundle were constructed recently by K.~Habermann. Here we study the spectral geometry aspects of these operators. In particular, we define the associated…
We define spin frames, with the aim of extending spin structures from the category of (pseudo-)Riemannian manifolds to the category of spin manifolds with a fixed signature on them, though with no selected metric structure. Because of this…
The quantum disc is used to define a noncommutative analogue of a dense coordinate chart and of left-invariant vector fields on quantum SU(2). This yields two twisted Dirac operators for different twists that are related by a gauge…
Quantum spaces with $\frak{su}(2)$ noncommutativity can be modelled by using a family of $SO(3)$-equivariant differential $^*$-representations. The quantization maps are determined from the combination of the Wigner theorem for $SU(2)$ with…