Related papers: Trace extensions, determinant bundles, and gauge g…
In this paper, we give two Lichnerowicz type formulas for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection. We also prove two Kastler-Kalau-Walze type theorems for twisted Dirac operators and…
The canonical and symmetrical energy-momentum tensors and their non-zero traces in Maxwell's theory on non-commutative spaces have been found. Dirac's quantization of the theory under consideration has been performed. I have found the…
This article is concerned with the analysis of Dirac operators $D$ twisted by ramified Euclidean line bundles $(Z,\mathfrak{l})$-motivated by their relation with harmonic $\mathbf{Z}/2\mathbf{Z}$ spinors, which have appeared in various…
We construct a noncommutative geometry with generalised `tangent bundle' from Fell bundle $C^*$-categories ($E$) beginning by replacing pair groupoid objects (points) with objects in $E$. This provides a categorification of a certain class…
In classical and quantum mechanical systems on manifolds with gauge-field fluxes, constants of motion are constructed from gauge-covariant extensions of Killing vectors and tensors. This construction can be carried out using a manifestly…
To supplement the already known classification of traces on classical pseudodifferential operators, we present a classification of traces on the algebras of odd-class pseudodifferential operators of non-positive order acting on smooth…
Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…
We consider on a spin manifold with boundary a Dirac operator $D_A$ with chiral boundary conditions, twisted by a unitary connection $A$. When $m$ is not in the chiral spectrum of $D_A$, we define an analogue of the Dirichlet-to-Neumann map…
We recall the emergence of a generalized gauge theory from a noncommutative Riemannian spin manifold, viz. a real spectral triple $(A,H,D;J)$. This includes a gauge group determined by the unitaries in the $*$-algebra $A$ and gauge fields…
We update our previous work on the description of twisted configurations for complex massless scalar field on the Kerr black holes as the sections of complex line bundles over the Kerr black hole topology. From physical point of view the…
We study differential invariants of linear differential operators and use them to find conditions for equivalence of differential operators acting in line bundles over smooth manifolds with respect to groups of authomorphisms.
We consider here the category of diffeological vector pseudo-bundles, and study a possible extension of classical differential geometric tools on finite dimensional vector bundles, namely, the group of automorphisms, the frame bundle, the…
In classical field theory, the composite fibred manifolds Y -> Z -> X provides the adequate mathematical formulation of gauge models with broken symmetries, e.g., the gauge gravitation theory. This work is devoted to connections on…
Let $E_1,\dots ,E_k$ and $E$ be natural vector bundles defined over the category $\Cal Mf_m^+$ of smooth oriented $m$--dimensional manifolds and orientation preserving local diffeomorphisms, with $m\geq 2$. Let $M$ be an object of $\Cal…
The article considers some concrete solutions to the Dirac equation coupled to a vector bundle with connection, arising in the study of Yang-Mills equations and vector bundles on Riemann surfaces.
The general purpose bitensorially gauge-covariant differentiation procedure set up in the preceding article is specialised to the particular case of bundles with nonlinear fibres that are endowed with a torsion free Riemannian or…
Noncommutative (NC) sphere is introduced as a quotient of the enveloping algebra of the Lie algebra su(2). Using the Cayley-Hamilton identities we introduce projective modules which are analogues of line bundles on the usual sphere (we call…
We review some of the geometry of the quantum projective plane with emphasis on the construction of a differential calculus and of the Dirac operator (of a spin^c-structure). We also report on anti-self-dual connections on line bundles, the…
The conformal anomaly and the Virasoro algebra are fundamental aspects of 2D conformal field theory and conformally covariant models in planar random geometry. In this article, we explicitly derive the Virasoro algebra from an…
In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that…