The Standard Model - the Commutative Case: Spinors, Dirac Operator and de Rham Algebra
Frank, Michael
arXiv, 0002045 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2000-02-23
Classification:  Mathematical Physics,  Mathematics - Differential Geometry,  Mathematics - Operator Algebras,  Mathematics - Symplectic Geometry 
@article{0002045,
     author = {Frank, Michael},
     title = {The Standard Model - the Commutative Case: Spinors, Dirac Operator and
  de Rham Algebra},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0002045}
}

Frank, Michael. The Standard Model - the Commutative Case: Spinors, Dirac Operator and
  de Rham Algebra. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0002045/