The Standard Model - the Commutative Case: Spinors, Dirac Operator and de Rham Algebra

Fuente: arXiv
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Main Author: Frank, Michael
Format: Preprint
Published: 2000
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author Frank, Michael
author_facet Frank, Michael
contents The present paper is a short survey on the mathematical basics of Classical Field Theory including the Serre-Swan' theorem, Clifford algebra bundles and spinor bundles over smooth Riemannian manifolds, Spin^C-structures, Dirac operators, exterior algebra bundles and Connes' differential algebras in the commutative case, among other elements. We avoid the introduction of principal bundles and put the emphasis on a module-based approach using Serre-Swan's theorem, Hermitian structures and module frames. A new proof (due to Harald Upmeier) of the differential algebra isomorphism between the set of smooth sections of the exterior algebra bundle and Connes' differential algebra is presented.
format Preprint
id arxiv_https___arxiv_org_abs_math_ph_0002045
institution arXiv
publishDate 2000
record_format arxiv
spellingShingle The Standard Model - the Commutative Case: Spinors, Dirac Operator and de Rham Algebra
Frank, Michael
Mathematical Physics
Differential Geometry
Operator Algebras
Symplectic Geometry
The present paper is a short survey on the mathematical basics of Classical Field Theory including the Serre-Swan' theorem, Clifford algebra bundles and spinor bundles over smooth Riemannian manifolds, Spin^C-structures, Dirac operators, exterior algebra bundles and Connes' differential algebras in the commutative case, among other elements. We avoid the introduction of principal bundles and put the emphasis on a module-based approach using Serre-Swan's theorem, Hermitian structures and module frames. A new proof (due to Harald Upmeier) of the differential algebra isomorphism between the set of smooth sections of the exterior algebra bundle and Connes' differential algebra is presented.
title The Standard Model - the Commutative Case: Spinors, Dirac Operator and de Rham Algebra
topic Mathematical Physics
Differential Geometry
Operator Algebras
Symplectic Geometry
url https://arxiv.org/abs/math-ph/0002045