Becchi-Rouet-Stora-Tyutin structure for the mixed Weyl-diffeomorphism residual symmetry

Abstract

In this paper, we show the compatibility of the so-called “dressing field method,” which allows a systematic reduction of gauge symmetries, with the inclusion of diffeomorphisms in the Becchi-Rouet-Stora-Tyutin (BRST) algebra of a gauge theory. The robustness of the scheme is illustrated on two examples where Cartan connections play a significant role. The former is General Relativity, while the latter concerns the second-order conformal structure where one ends up with a BRST algebra handling both the Weyl residual symmetry and diffeomorphisms of spacetime. We thereby provide a geometric counterpart to the BRST cohomological treatment used in Boulanger [J. Math. Phys. 46, 053508 (2005)] in the construction of a Weyl covariant tensor calculus.