BRST-invariant boundary conditions and strong ellipticity

Abstract

The quantisation of gauge theories usually procedes through the introduction of ghost fields and BRST symmetry. In the case of quantum gravity in the presence of boundaries, the BRST-invariant boundary value problem for the gauge field operators is non-elliptic, and consequently the definition of the effective action using heat-kernel techniques becomes problematic. This paper examines general classes of BRST-invariant boundary conditions and presents new boundary conditions for quantum gravity which fix the extrinsic curvature on the boundary and lead to a well-defined effective action. This prompts a discussion of the wider issue of non-ellipticity in BRST-invariant boundary value problems and when the use of gauge-fixing terms on the boundary can resolve the issue.

16 pages, revtex

References in corpus (3)

• Boundary Conditions for Interacting Membranes
• Quantum Effective Action in Spacetimes with Branes and Boundaries: Diffeomorphism Invariance
• Effective action and heat kernel in a toy model of brane-induced gravity

Cited by in corpus (7)

• Physical renormalization schemes and asymptotic safety in quantum gravity
• Boundary dynamics in gravitational theories
• On the renormalization of the Gibbons-Hawking boundary term
• On the resilience of the gravitational variational principle under renormalization
• Constrained field theories on spherically symmetric spacetimes with horizons
• Hamiltonian BRST formalism for gauge fields on black hole spacetimes
• The Gribov phenomenon in flat and curved spaces