SpinT structure and Dirac operator on Riemannian manifolds
Senay Bulut, Ali Kemal Erkoca
TL;DR
This paper introduces the SpinT group, constructs the associated spinor bundle and Dirac operator on Riemannian manifolds, and derives a Schrodinger-Lichnerowicz-type formula to analyze their properties.
Contribution
It defines the SpinT group, constructs the spinor bundle and Dirac operator, and derives a new formula relating these operators on Riemannian manifolds.
Findings
Properties of the SpinT group are established.
Construction of the spinor bundle S using SpinT representation.
Derivation of a Schrodinger-Lichnerowicz-type formula.
Abstract
In this paper, we describe the group SpinT (n) and give some properties of this group. We construct SpinT spinor bundle S by means of the spinor representation of the group SpinT (n) and define covariant derivative operator and Dirac operator on S. Finally, Schrodinger-Lichnerowicz-type formula is derived by using these operators.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Algebraic and Geometric Analysis · Advanced Algebra and Geometry