2023/09/26 by M. P. Hobson, A. Lasenby, Hobson, Michael +3 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2309.14783
openalex publication_date 2023/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A variational principle for gauge theories of gravity is presented, which maintains manifest covariance under the symmetries to which the action is invariant, throughout the calculation of the equations of motion and conservation laws. This is performed by deriving explicit manifestly covariant expressions for the Euler--Lagrange variational derivatives and Noether's theorems for a generic action of the form typically assumed in gauge theories of gravity. The approach is illustrated by application to two scale-invariant gravitational gauge theories, namely Weyl gauge theory (WGT) and the recently proposed `extended' Weyl gauge theory (eWGT), where the latter may be considered as a novel gauging of the conformal group, but the method can be straightforwardly applied to other theories with smaller or larger symmetry groups. The approach also enables one easily to establish the relationship between manifestly covariant forms of variational derivatives obtained when one or more of the gauge field strengths is set to zero either before or after the variation is performed. This is illustrated explicitly for both WGT and eWGT in the case where the translational gauge field strength (or torsion) is set to zero before and after performing the variation, respectively.