Connections and the Dirac operator on spinor bundles

@article{Trautman2008ConnectionsAT,
  title={Connections and the Dirac operator on spinor bundles},
  author={Andrzej Trautman},
  journal={Journal of Geometry and Physics},
  year={2008},
  volume={58},
  pages={238-252}
}
  • A. Trautman
  • Published 1 February 2008
  • Mathematics
  • Journal of Geometry and Physics
Conformal Geometry of the Supercotangent and Spinor Bundles
We study the actions of local conformal vector fields $${X \in {\rm conf}(M,g)}$$ on the spinor bundle of (M, g) and on its classical counterpart: the supercotangent bundle $${\mathcal{M}}$$ of (M,
Real spinor bundles and real Lipschitz structures
We obtain the topological obstructions to existence of a bundle of irreducible real Clifford modules over a pseudo-Riemannian manifold $(M,g)$ of arbitrary dimension and signature and prove that
Holomorphic family of Dirac-Coulomb Hamiltonians in arbitrary dimension
We study massless 1-dimensional Dirac-Coulomb Hamiltonians, that is, operators on the half-line of the form Dω,λ := [ − x −∂x ∂x −λ−ω x ] . We describe their closed realizations in the sense of the
Spin Frame Transformations and Dirac Equations
  • R. Noris, L. Fatibene
  • Mathematics
    International Journal of Geometric Methods in Modern Physics
  • 2021
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
Geometric algebra techniques in flux compactifications (II)
A bstractWe study constrained generalized Killing spinors over the metric cone and cylinder of a (pseudo-)Riemannian manifold, developing a toolkit which can be used to investigate certain problems
Structures of spinors fiber bundles with special relativity of Dirac operator using the Clifford algebra
  • Y. Hassan
  • Mathematics
    Demonstratio Mathematica
  • 2021
Abstract The purpose of this article is to demonstrate how to use the mathematics of spinor bundles and their category. We have used the methods of principle fiber bundles obey thorough solid
Nilpotent symmetries as a mechanism for Grand Unification
Abstract In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar
Tensor- and spinor-valued random fields with applications to continuum physics and cosmology
In this paper, we review the history, current state-of-art, and physical applications of the spectral theory of two classes of random functions. One class consists of homogeneous and isotropic random
Four-vector vs. four-scalar representation of the Dirac wave function
In a Minkowski spacetime, one may transform the Dirac wave function under the spin group, as one transforms coordinates under the Poincare group. This is not an option in a curved spacetime.
...
...

References

SHOWING 1-10 OF 33 REFERENCES
Spin Spaces, Lipschitz Groups, and Spinor Bundles
It is shown that every bundle Σ → M of complex spinormodules over the Clifford bundle Cl(g) of a Riemannian space(M, g) with local model (V, h)is associated with an lpin(‘Lipschitz’) structure on M,
THE DIRAC OPERATOR ON HYPERSURFACES
Odd-dimensional Riemannian spaces that are non-orientable, but have a pin structure, require the consideration of the twisted adjoint representation of the corresponding pin group. It is shown here
Spinors and the Dirac operator on hypersurfaces. I. General theory
It is shown that a hypersurface immersed isometrically into the Euclidean space Rn+1, where n=2ν or 2ν+1, has a pin structure such that the associated bundle of 2ν‐component spinors is trivial. This
The Srní lectures on non-integrable geometries with torsion
This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connec- tions with torsion, and to discuss recent aspects of
CLIFFORD MODULES
  • A.
  • Mathematics
  • 1964
The purpose of the paper is to undertake a detailed investigation of the role of Clifford algebras and spinors in the K&theory of real vector bundles. On the one hand the use of Clifford algebras
Dirac Operators in Riemannian Geometry
Clifford algebras and spin representation Spin structures Dirac operators Analytical properties of Dirac operators Eigenvalue estimates for the Dirac operator and twistor spinors Seiberg-Witten
The quantum theory of the electron
The new quantum mechanics, when applied to the problem of the structure of the atom with point-charge electrons, does not give results in agreement with experiment. The discrepancies consist of
Encyclopedia of Mathematical Physics
Classical, Conformal and Topological Field Theory Classical Mechanics Condensed Matter Physics and Optics Differential Geometry Dirac Operators Dynamical Systems Fluid Dynamics Functional Analysis
Elektron und gravitation. I
Abstract Einleitung. Verhaltnis der allgemeinen Relativitatstheorie zu den quanten-theoretischen Feldgleichungen des spinnenden Elektrons: Masse, Eichinvarianz, Fernparallelismus. Zu erwartende
...
...