Related papers: A note on metric connections for chiral and Dirac …

In this paper we define a Dirichlet-to-Neumann map for a twisted Dirac Laplacian acting on bundle-valued spinors over a spin manifold. We show that this map is a pseudodifferential operator of order 1 whose symbol determines the Taylor…

We describe how to construct chiral fermion mass terms using Dirac-Kahler (DK) spinors. Classical massive DK spinors are shown to be equivalent to four generations of Dirac spinors with equal mass coupled to a background U(2,2) gauge field.…

We give a geometrical construction of Connes spectral triples or noncommutative Dirac operators $D$ starting with a bimodule connection on the proposed spinor bundle. The theory is applied to the example of $M_2(\Bbb C)$, and also applies…

Quaternion Dirac equation has been analyzed and its supersymetrization has been discussed consistently. It has been shown that the quaternion Dirac equation automatically describes the spin structure with its spin up and spin down…

Based on the observation that Cacic [10]'s characterization of almost commutative spectral triples as Clifford module bundles can be pushed to endomorphim algebras of Dirac bundles, with the geometric Dirac operator related to the Dirac…

In this paper we introduce the Dirac and spin-Dirac operators associated to a connection on Riemann-Cartan space(time) and standard Dirac and spin-Dirac operators associated with a Levi-Civita connection on a Riemannian (Lorentzian)…

In this paper, we construct the index bundle gerbe of a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we construct a geometric bundle gerbe called the caloron bundle gerbe, which comes…

We discuss the most general form of Dirac equation in the non$-$Riemannian spacetimes containing curvature, torsion and non$-$metricity. It includes all bases of the Clifford algebra $cl(1,3)$ within the spinor connection. We adopt two…

In this largely expository paper we give a self-contained treatment of the Dirac operator. Emphasizing the algebraic point of view we first sketch the necessary prerequisites from Clifford algebras and their representations and then define…

The vortical susceptibility of chiral condensate is derived in two ways. First we obtain this using the spectrum of the Dirac operator in a metric of a curved space-time, which corresponds to rotation. Second we come to the expression for…

We present a universal Dirac operator for noncommutative spin and spin^c bundles over fuzzy complex projective spaces. We give an explicit construction of these bundles, which are described in terms of finite dimensional matrices, calculate…

We give a classification of $1^{st}$ order invariant differential operators acting between sections of certain bundles associated to Cartan geometries of the so called metaplectic contact projective type. These bundles are associated via…

Dirac equation is written in a non-Riemannian spacetime with torsion and non-metricity by lifting the connection from the tangent bundle to the spinor bundle over spacetime. Foldy-Wouthuysen transformation of the Dirac equation in a…

This paper studies the behavior of sequences of solutions to Seiberg-Witten like equations for a pair consisting of a Hermitian connection on a line bundle over a 4-dimensional manifold and a section of the self-dual spinor bundle of a…

We introduce the notion of matched pairs of Courant algebroids and give several examples arising naturally from complex manifolds, holomorphic Courant algebroids, and certain regular Courant algebroids. We consider the matched sum of two…

We propose an ansatz for the commutative canonical spin_c Dirac operator on CP^2 in a global geometric approach using the right invariant (left action-) induced vector fields from SU(3). This ansatz is suitable for noncommutative…

We give some remarks on twisted determinant line bundles and Chern-Simons topological invariants associated with real hyperbolic manifolds. Index of a twisted Dirac operator is derived. We discuss briefly application of obtained results in…

A metric tree is a tree whose edges are viewed as line segments of positive length. The Dirac operator on such tree is the operator which operates on each edge, complemented by the matching conditions at the vertices which were given by…

We present a new staggered discretization of the Dirac operator. Doubling gives only a doublet of Dirac fermions which we propose to interpret as a physical (lepton or quark) doublet. If coupled with gauge fields, an $(1+\gamma^5)$ chiral…

Let $G$ be a connected real reductive group with maximal compact subgroup $K$ of equal rank, and let $\mathscr M$ be the category of Harish-Chandra modules for $G$. We relate three differentely defined pairings between two finite length…