Hearing the shape of inequivalent spin structures and exotic Dirac operators

Abstract

Exotic spinor fields arise from inequivalent spin structures on non-trivial topological manifolds, $M$. This induces an additional term in the Dirac operator, defined by the cohomology group $H^1(M,{\mathbb{Z}}_2)$ that rules a Cech cohomology class. This formalism is extended for manifolds of any finite dimension, endowed with a metric of arbitrary signature. The exotic corrections to heat kernel coefficients, relating spectral properties of exotic Dirac operators to the geometric invariants of $M$, are derived and scrutinized.

arXiv comment30 pages

References in corpus (33)

• Heat kernel expansion: user's manual
• Where are ELKO Spinor Fields in Lounesto Spinor Field Classification?
• Self-interacting Elko dark matter with an axis of locality
• Index-free Heat Kernel Coefficients
• Classification of Singular Spinor Fields and Other Mass Dimension One Fermions
• Dynamical dispersion relation for ELKO dark spinor fields
• Exotic Dark Spinor Fields
• Conformal Gravity with the most general ELKO Matter
• Dirac spinors in Bianchi-I f(R)-cosmology with torsion
• The quadratic spinor Lagrangian, axial torsion current, and generalizations
• The Bundles of Algebraic and Dirac-Hestenes Spinor Fields
• On the bilinear covariants associated to mass dimension one spinors
• Spinor Fields Classification in Arbitrary Dimensions and New Classes of Spinor Fields on 7-Manifolds
• New Spinor Fields on Lorentzian 7-Manifolds
• Questing for Algebraic Mass Dimension One Spinor Fields
• Constraints on mass dimension one fermionic dark matter from the Yukawa interaction
• A generally-relativistic gauge classification of the Dirac fields
• Dirac fields in f(R)-gravity with torsion
• Effective lagrangian for a mass dimension one fermionic field in curved spacetime
• Extended Grassmann and Clifford algebras
• Further investigation of mass dimension one fermionic duals
• Heat-kernel approach for scattering
• Constraints on mapping the Lounesto's Classes
• Exotic Elko on String-Like Defects in Six Dimensions
• A hint towards mass dimension one Flag-dipole spinors
• Some Remarks on dual helicity flag-dipole spinors
• Revisiting pinors, spinors and orientability
• New fermions in the bulk
• Quantum heat traces
• New spinor classes on the Graf-Clifford algebra
• Type-4 spinors: transmuting from Elko to single-helicity spinors
• Exotic Spinorial Structure and Black Holes in General Relativity
• The Restricted Inomata-McKinley spinor-plane, homotopic deformations and the Lounesto classification

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• Foundational aspects of spinor structures and exotic spinors