Related papers: Dominant energy condition and spinors on Lorentzia…

We provide an alternative approach to relativistic dynamics based on the Feshbach projection technique. Instead of directly studying the Dirac equation, we derive a two-component equation for the upper spinor. This approach allows one to…

I begin by explaining how Riemannian geometry can be understood in terms of principal fibre bundles and connections thereon. I then introduce and motivate the definition of a spinor structure in terms of familiar geometrical ideas. The…

We revisit the quantum lattice gas model of a spinor quantum field theory-the smallest scale particle dynamics is partitioned into unitary collide and stream operations. The construction is covariant (on all scales down to a small length…

In LM, we proved a family version of the famous Witten rigidity theorems and several family vanishing theorems for elliptic genera. In this paper, we gerenalize our theorems LM in two directions. First we establish a family rigidity theorem…

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…

We study Dirac operators on resolutions of Riemannian orbifolds by developing a uniform elliptic theory. The key idea is to view orbifolds as conically fibred singular (CFS) spaces and resolve them by gluing asymptotically conical…

Let $M$ be pseudo-Riemannian homogeneous Einstein manifold of finite volume, and suppose a connected Lie group $G$ acts transitively and isometrically on $M$. In this situation, the metric on $M$ induces a bilinear form…

We study perturbed Dirac operators of the form $ D_s= D + s{\cal A} :\Gamma(E)\rightarrow \Gamma(F)$ over a compact Riemannian manifold $(X, g)$ with symbol $c$ and special bundle maps ${\cal A} : E\rightarrow F$ for $s>>0$. Under a simple…

Dirac-Coulomb type differential equation and its solution relativistic exponential-type spinor orbitals are introduced. They provide a revised form for operator invariants, namely Dirac invariants, simplifying the treatment of the angular…

Let $X=\mathbb{C}\times\Sigma$ be the product of the complex plane and a compact Riemann surface. We establish a classification theorem of solutions to the Seiberg-Witten equation on $X$ with finite analytic energy. The spin bundle $S^+\to…

In this paper we apply classical and recent techniques from quaternionic analysis using parabolic Dirac type operators and related Teodorescu and Cauchy-Bitzadse type operators to set up some analytic representation formulas for the…

Suppose that $\Sigma=\partial M$ is the $n$-dimensional boundary of a connected compact Riemannian spin manifold $( M,\langle\;,\;\rangle)$ with non-negative scalar curvature, and that the (inward) mean curvature $H$ of $\Sigma$ is…

Using the index theory for twisted Dirac operators acting on sections of Lipschitz bundles over non-compact manifolds, we prove Llarull-type comparison results in scalar curvature geometry. They apply to spin Riemannian manifolds with…

In this article we investigate the restrictions imposed by the dominant energy condition (DEC) on the topology and conformal type of \textsl{possibly non-compact} marginally outer-trapped surfaces (thus extending Hawking's classical theorem…

By using the Ljusternik-Schnirelman principle, we establish the existence of a nondecreasing sequence of nonnegative eigenvalues for the p-Dirac operator on compact spin manifold. Using the biorthogonal system theory on separable Banach…

The holonomy group of an (n+2)-dimensional simply-connected, indecomposable but non-irreducible Lorentzian manifold (M,h) is contained in the parabolic group $(\mathbb{R} \times SO(n))\ltimes \mathbb{R}^n$. The main ingredient of such a…

A minimal-length scenario can be considered as an effective description of quantum gravity effects. In quantum mechanics the introduction of a minimal length can be accomplished through a generalization of Heisenberg's uncertainty…

Inspired by the classical Poincar\'e criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the variational properties of periodic…

We develop a formula for the equivariant index of a twisted Dirac operator on a compact globally hyperbolic spacetime with timelike boundary on which a group acts isometrically, subject to APS boundary conditions. The formula is the same as…

We show that knowledge of the source-to-solution map for the fractional Dirac operator acting over sections of a Hermitian vector bundle over a smooth closed connencted Riemannian manifold of dimension $m\geq 2$ determines uniquely the…