Gravity with more or less gauging

Abstract

General Relativity is usually formulated as a theory with gauge invariance under the diffeomorphism group, but there is a 'dilaton' formulation where it is in addition invariant under Weyl transformations, and a 'unimodular' formulation where it is only invariant under the smaller group of special diffeomorphisms. Other formulations with the same number of gauge generators, but a different gauge algebra, also exist. These different formulations provide examples of what we call 'inessential gauge invariance', 'symmetry trading' and 'linking theories'; they are locally equivalent, but may differ when global properties of the solutions are considered. We discuss these notions in the Lagrangian and Hamiltonian formalism.In the four-dimensional case Z N is one half of the squared reduced Planck mass M 2 P = (8πG) −1 .

A link that matters: towards phenomenological tests of unimodular asymptotic safety

“…Thus it is of interest to understand the resulting differences in the interplay with matter. For a clear discussion of the relation of various symmetry-restrictions on gravity at the classical level, see [19].…”

Unfree gauge symmetry in the Hamiltonian formalism

“…Even in well-studied models, like unimodular gravity, the transversality condition on the diffeomorphism parameters is not evident from the viewpoint of the Poisson algebra of Hamiltonian constraints. This problem is noticed in the literature, see [7] and references therein.…”

“…The most known example of unfree gauge symmetry is provided by unimodular gravity where the diffeomorphism parameters ǫ µ are constrained by transversality condition ∇ µ ǫ µ = 0. For discussion of consequences of transversality condition in the unimodular gravity and various extensions, see [3], [4], [5], [6], [7], [8], [9], [10], [11] and references therein. More examples of unfree gauge symmetry can be found among multifarious higher spin field theories, see [12], [13], [14], [15].…”

Towards metric-affine quantum gravity

“…This, however, a See [1] for a comprehensive overview. b Alternatively, one can think of them as the result of applying the Stückelberg trick to unimodular gravity, which is the formulation with the least number of fields that is still local [2]. c For simplicity we consider here pure gravity without matter.…”