## 34 Citations

### Conformal Geometry of the Supercotangent and Spinor Bundles

- Mathematics
- 2012

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

- MathematicsAsian Journal of Mathematics
- 2019

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…

### Spin Frame Transformations and Dirac Equations

- MathematicsInternational 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)

- Mathematics
- 2013

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

- MathematicsDemonstratio 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

- MathematicsJournal of High Energy Physics
- 2021

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

- Mathematics
- 2021

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

- Mathematics
- 2012

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.…

### An index theorem on asymptotically static spacetimes with compact Cauchy surface

- Mathematics
- 2021

. We consider the Dirac operator on asymptotically static Lorentzian manifolds with an odd-dimensional compact Cauchy surface. We prove that if Atiyah– Patodi–Singer boundary conditions are imposed…

## References

SHOWING 1-10 OF 29 REFERENCES

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- Mathematics
- 1999

It is shown that every bundle Σ → M of complex spinor modules 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…

### CLIFFORD ALGEBRAS AND THEIR REPRESENTATIONS

- Mathematics
- 2007

Introductory and historical remarks Clifford (1878) introduced his ‘geometric algebras’ as a generalization of Grassmann algebras, complex numbers and quaternions. Lipschitz (1886) was the first to…

### THE DIRAC OPERATOR ON HYPERSURFACES

- Mathematics
- 1995

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

- Mathematics
- 1992

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

- Mathematics
- 2006

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…

### Dirac Operators in Riemannian Geometry

- Mathematics
- 2000

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

- Physics
- 1928

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

- Physics, Mathematics
- 2006

Classical, Conformal and Topological Field Theory Classical Mechanics Condensed Matter Physics and Optics Differential Geometry Dirac Operators Dynamical Systems Fluid Dynamics Functional Analysis…