{"work":{"id":"70339513-7e2e-49b4-b7ee-3d84e4e5ea0b","openalex_id":null,"doi":null,"arxiv_id":"gr-qc/9402012","raw_key":null,"title":"Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance","authors":null,"authors_text":"F","year":1994,"venue":"gr-qc","abstract":"In Einstein's gravitational theory, the spacetime is Riemannian, that is, it has vanishing torsion and vanishing nonmetricity (covariant derivative of the metric). In the gauging of the general affine group ${A}(4,R)$ and of its subgroup ${GL}(4,R)$ in four dimensions, energy--momentum and hypermomentum currents of matter are canonically coupled to the one--form basis and to the connection of a metric--affine spacetime with nonvanishing torsion and nonmetricity, respectively. Fermionic matter can be described in this framework by half--integer representations of the $\\overline{SL}(4,R)$ covering subgroup. --- We set up a (first--order) Lagrangian formalism and build up the corresponding Noether machinery. For an arbitrary gauge Lagrangian, the three gauge field equations come out in a suggestive Yang-Mills like form. The conservation--type differential identities for energy--momentum and hypermomentum and the corresponding complexes and superpotentials are derived. Limiting cases such as the Einstein--Cartan theory are discussed. In particular we show, how the ${A}(4,R)$ may ``break down'' to the Poincar\\'e (inhomogeneous Lorentz) group. In this context, we present explicit models for a symmetry breakdown in the cases of the Weyl (or homothetic) group, the ${SL}(4,R)$, or the ${GL}(4,R)$.","external_url":"https://arxiv.org/abs/gr-qc/9402012","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-05-25T19:21:09.533746+00:00","pith_arxiv_id":"gr-qc/9402012","created_at":"2026-05-11T12:56:15.243351+00:00","updated_at":"2026-05-25T19:21:09.533746+00:00","title_quality_ok":false,"display_title":null,"render_title":"Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance"},"hub":{"state":{"work_id":"70339513-7e2e-49b4-b7ee-3d84e4e5ea0b","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":14,"external_cited_by_count":null,"distinct_field_count":4,"first_pith_cited_at":"2019-06-21T02:21:47+00:00","last_pith_cited_at":"2026-05-16T08:15:03+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-05-26T00:06:06.577450+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":2}],"polarity_counts":[{"context_polarity":"background","n":2}],"runs":{},"summary":{},"graph":{},"authors":[]}}