Novel symmetries in Weyl-invariant gravity with massive gauge field

Abstract

The background field method is used to linearize the Weyl-invariant scalar-tensor gravity, coupled with a Stückelberg field. For a generic background metric, this action is found not to be invariant, under both a diffeomorphism and generalized Weyl symmetry, the latter being a combination of gauge and Weyl transformations. Interestingly, the quadratic Lagrangian, emerging from a background of Minkowski metric, respects both transformations independently. The Becchi-Rouet-Stora-Tyutin symmetry of scalar-tensor gravity coupled with a Stückelberg-like massive gauge particle, possessing a diffeomorphism and generalized Weyl symmetry, reveals that in both cases negativenorm states with unphysical degrees of freedom do exist. We then show that, by combining diffeomorphism and generalized Weyl symmetries, all the ghost states decouple, thereby removing the unphysical redundancies of the theory. During this process, the scalar field does not represent any dynamic mode, yet modifies the usual harmonic gauge condition through non-minimal coupling with gravity.

Conservation law for massive scale-invariant photons in Weyl-invariant gravity

“…is obtained, merely stating that all fields are dynamically not independent [34]. Intuitively, coupling with gauge field can make the scalar field 'massive', but that mass will be gauge-dependent in general, as is well-known from the self-energy corrections in quantum electrodynamics (QED) [35].…”

Quantum Gauge Symmetry of Reducible Gauge Theory

“…On the other hand, the Becchi-Rouet-Stora-Tyutin (BRST) formulation [31,32] is a subject of vast interests [33,34], as it leads to unitarity and renormalizability of the gauge theories. The BSRT symmetry has found dual analogue of Hodge theory [35,36].…”