Kavli Affiliate: Anthony Lasenby
| First 5 Authors: Michael Hobson, Anthony Lasenby, Will Barker, ,
| Summary:
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.
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