Dirac Sources for Nonmetricity and Torsion in Metric-affine Gravity
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914403896524800 |
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| author | Wheeler, James T. |
| author_facet | Wheeler, James T. |
| contents | Metric-affine gravity (GL(4) gauge theory) in 4-dimensions is coupled to a spacetime Dirac source field using the isomorphisms of the Lie algebra gl(4) to the Clifford algebras Cl(3,1) and Cl(2,2). A simple transformation relates the generators of Cl(3,1) to a real representation of Cl(2,2), while the real representation of Cl(2,2) serves directly as a basis for the Lie algebra gl(4). Therefore, although GL(4) does not contain a spinor representation of the Lorentz group, expanding its Lie algebra in the Cl(2,2) basis gives a Clifford valued connection with well-defined coupling to Dirac spinors. Variation of the expansion coefficients gives new Dirac sources for both torsion and nonmetricity, separated by identifying the so(3,1) basis within the gl(4) basis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_09013 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dirac Sources for Nonmetricity and Torsion in Metric-affine Gravity Wheeler, James T. General Relativity and Quantum Cosmology High Energy Physics - Theory Metric-affine gravity (GL(4) gauge theory) in 4-dimensions is coupled to a spacetime Dirac source field using the isomorphisms of the Lie algebra gl(4) to the Clifford algebras Cl(3,1) and Cl(2,2). A simple transformation relates the generators of Cl(3,1) to a real representation of Cl(2,2), while the real representation of Cl(2,2) serves directly as a basis for the Lie algebra gl(4). Therefore, although GL(4) does not contain a spinor representation of the Lorentz group, expanding its Lie algebra in the Cl(2,2) basis gives a Clifford valued connection with well-defined coupling to Dirac spinors. Variation of the expansion coefficients gives new Dirac sources for both torsion and nonmetricity, separated by identifying the so(3,1) basis within the gl(4) basis. |
| title | Dirac Sources for Nonmetricity and Torsion in Metric-affine Gravity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.09013 |