Canonical Vielbeins for General Relativity: D + 1 Decomposition and Constraint Analysis
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917535524323328 |
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| author | Flinckman, Joakim Blixt, Daniel |
| author_facet | Flinckman, Joakim Blixt, Daniel |
| contents | We provide a self-contained derivation of the Hamiltonian formulation of General Relativity in vielbein variables in $d=D+1$ dimensions. Starting from the Einstein--Hilbert action in a standard metric $D+1$ decomposition, we derive Lorentz- and $\mathrm{SO}(D)$-covariant phase-space actions, identify the primary Lorentz constraints, and obtain the Hamiltonian and momentum constraints. We compute the resulting first-class constraint algebra, relate the vielbein and metric phase-space formulations, and discuss the rotation/boost decomposition. In particular, we construct the boost generator in the $\mathrm{SO}(D)$-covariant formulation, thereby recovering full local Lorentz symmetry. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_18491 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Canonical Vielbeins for General Relativity: D + 1 Decomposition and Constraint Analysis Flinckman, Joakim Blixt, Daniel General Relativity and Quantum Cosmology High Energy Physics - Theory We provide a self-contained derivation of the Hamiltonian formulation of General Relativity in vielbein variables in $d=D+1$ dimensions. Starting from the Einstein--Hilbert action in a standard metric $D+1$ decomposition, we derive Lorentz- and $\mathrm{SO}(D)$-covariant phase-space actions, identify the primary Lorentz constraints, and obtain the Hamiltonian and momentum constraints. We compute the resulting first-class constraint algebra, relate the vielbein and metric phase-space formulations, and discuss the rotation/boost decomposition. In particular, we construct the boost generator in the $\mathrm{SO}(D)$-covariant formulation, thereby recovering full local Lorentz symmetry. |
| title | Canonical Vielbeins for General Relativity: D + 1 Decomposition and Constraint Analysis |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2602.18491 |