The Standard Model - the Commutative Case: Spinors, Dirac Operator and de Rham Algebra
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arXiv
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| Format: | Preprint |
| Published: |
2000
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| _version_ | 1866915276334825472 |
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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 |