Spinor Representations of Surfaces in 4-Dimensional Pseudo-Riemannian Manifolds

Vadim V. Varlamov

Spinor Representations of Surfaces in 4-Dimensional Pseudo-Riemannian Manifolds

Differential Geometry 2007-05-23 v1 Mathematical Physics math.MP

Authors: Vadim V. Varlamov

Abstract

Spinor representations of surfaces immersed into 4-dimensional pseudo-riemannian manifolds are defined in terms of minimal left ideals and tensor decompositions of Clifford algebras. The classification of spinor fields and Dirac operators on the immersed surfaces is given. The Dirac-Hestenes spinor field on surfaces immersed into Lorentzian manifolds and on surfaces conformally immersed into Minkowski spacetime is defined.

Keywords

spinor representation clifford algebra pseudo-riemannian manifold dirac operator immersed surface dirac-hestenes spinor

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@article{arxiv.math/0004056,
  title  = {Spinor Representations of Surfaces in 4-Dimensional Pseudo-Riemannian Manifolds},
  author = {Vadim V. Varlamov},
  journal= {arXiv preprint arXiv:math/0004056},
  year   = {2007}
}

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37 pages, LaTeX2e

Spinor Representations of Surfaces in 4-Dimensional Pseudo-Riemannian Manifolds

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