Related papers: Differential operator Dirac structures

We use the $\zeta$-function regularization and an integral representation of the complex power of a pseudo differential operator, to give an unambiguous definition of the determinant of the Dirac operator. We bring this definition to a…

First, we study the subskewfield of rational pseudodifferential operators over a differential field K generated in the skewfield of pseudodifferential operators over K by the subalgebra of all differential operators. Second, we show that…

Let S be a flat surface of genus g with cone type singularities. Given a bipartite graph G isoradially embedded in S, we define discrete analogs of the 2^{2g} Dirac operators on S. These discrete objects are then shown to converge to the…

Let ${\mathfrak o}$ be a complete discrete valuation ring of mixed characteristic $(0,p)$ and ${\mathfrak X}_0$ a smooth formal scheme over the formal spectrum of ${\mathfrak o}$. Given an admissible formal blow-up ${\mathfrak X}$ of…

Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints.

This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators. These relations, including various…

Discrete versions of the Laplace and Dirac operators haven been studied in the context of combinatorial models of statistical mechanics and quantum field theory. In this paper we introduce several variations of the Laplace and Dirac…

We describe a canonical form for linear differential operators that are formally self-adjoint or formally skew-adjoint.

In this paper we study some operators associated to the Rarita-Schwinger operators. They arise from the difference between the Dirac operator and the Rarita-Schwinger operators. These operators are called remaining operators. They are based…

In this work we consider the two-dimensional Dirac operator with general local singular interactions supported on a closed curve. A systematic study of the interaction is performed by decomposing it into a linear combination of four…

New sufficient conditions and necessary conditions are developed for two skew diagrams to give rise to the same skew Schur function. The sufficient conditions come from a variety of new operations related to ribbons (also known as border…

In this thesis, we show the existence of a sequence of differential operators starting with with the Dirac operator in k Clifford variables, $D=(D_1,..., D_k)$, where $D_i=\sum_j e_j\cdot \partial_{ij}: C^\infty((\R^n)^k,\S)\to…

This is a survey article on a known generalization of Dirac-type operators to transverse operators called basic Dirac operators on Riemannian foliations, which are smooth foliations that have a transverse geometric structure. Construction…

We give the description of self-adjoint regular Dirac operators, on $[0, \pi]$, with the same spectra.

We study the notion of a Dirac operator in the framework of twist-deformed noncommutative geometry. We provide a number of well-motivated candidate constructions and propose a minimal set of axioms that a noncommutative Dirac operator…

We study the exterior derivative as a symmetric unbounded operator on square integrable 1-forms on a 3D bounded domain $D$. We aim to identify boundary conditions that render this operator self-adjoint. By the symplectic version of the…

We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a $(2+1)$-dimensional Riemann (curved) spacetime.…

This paper is a follow-up on the \emph{noncommutative differential geometry on infinitesimal spaces} [15]. In the present work, we extend the algebraic convergence from [15] to the geometric setting. On the one hand, we reformulate the…

Let $D_t$, $t \in [0,1]$ be an arbitrary 1-parameter family of Dirac type operators on a two-dimensional disk with $m-1$ holes. Suppose that all operators $D_t$ have the same symbol, and that $D_1$ is conjugate to $D_0$ by a scalar gauge…

We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis where derivatives are linear functions on abstract vectors rather than being limited to scalars,…