相关论文: Foundational aspects of spinor structures and exot…

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…

We present new parametrizations of elements of spinor and orthogonal groups of dimension 4 using Grassmann exterior algebra. Theory of spinor groups is an important tool in theoretical and mathematical physics namely in the Dirac equation…

As a means of examining the section condition and its possible solutions and relaxations, we perform twistor transforms related to versions of exceptional field theory with Minkowski signature. The spinor parametrisation of the momenta…

The aim of the lectures is to introduce first-year Ph.D. students and research workers to the theory of the Dirac operator, spinor techniques, and their relevance for the theory of eigenvalues in Riemannian geometry. Topics: differential…

This note contains some comments on a recent paper by Friedman on two-component spinors in spacetimes which do not admit a time-orientation, and is intended to clarify the relation of the work reported in that paper to previous literature.

Relativistic spin-1/2 particles in curved spacetime are naturally described by Dirac theory, which is a dynamical and Lorentz-invariant field theory. In this work, we propose a non-dynamical fermion theory in 3+1 dimensions dubbed spinor…

We study spinor field theories as an origin to induce space-time evolution. Self-interacting spinor fields with canonical and non-canonical kinetic terms are considered in a Friedman-Robertson-Walker universe. The deceleration parameter is…

In our Solar system, spin-orbit coupling is a common phenomenon in binary asteroid systems, where the mutual orbits are no longer invariant due to exchange of angular momentum between translation and rotation. In this work, dynamical…

We explore new aspects of internal fermionic shifting symmetries, present in physical systems such as free Dirac spinors and p-form tensor-spinor fields. We propose a novel procedure to gauge these global symmetries, which also introduces a…

We consider spinorial fields in polar form to deduce their respective tensorial connection in various physical situations: we show that in some cases the tensorial connection is a useful tool, instead in other cases it arises as a necessary…

The standard spinor connection in curved space-time is represented in a compact form. In this form the calculation is complicated, and its physical effects are concealed. In this paper, we split spinor connection into two vectors…

We look at smooth manifolds equipped with a possibly singular Riemannian metric. We give sufficient conditions for the existence of scalar curvature measures and Dirac operators.

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…

This paper relates skein spaces based on the Kauffman bracket and spin structures. A spin structure on an oriented 3-manifold provides an isomorphism between the skein space for parameter A and the skein space for parameter -A. There is an…

The interior structure of arbitrary sets of quaternion units is analyzed using general methods of the theory of matrices. It is shown that the units are composed of quadratic combinations of fundamental objects having a dual mathematical…

Two forms of anomalies for chiral spinors living on submanifolds of the spacetime are obtained from the integrality theorem for immersions. The first form of the chiral anomaly is the usual for chiral spinors living on D-brane and O-plane…

In this paper, we analyze some properties regarding singular spinors and how they are connected. The method employed here consists of mapping the spinorial structure and also the adjoint structure. Such a mathematical device is useful to…

Operator fields in the bundle of Dirac spinors and their conversion to spatial fields are considered. Some commutator equations are studied with the use of the conversion technique.

When spacetime is considered as a subspace of a wider complex spacetime manifold, there is a mismatch of the elementary linear representations of their symmetry groups, the real and complex Poincar\'{e} groups. In particular, no spinors are…

Extending the investigations about the theory of duals, we analyze duals built up with the aid of discrete symmetry operators. We scrutinize algebraic and physical constraints (encompassing them in a theoretical scope) in order to verify…