1301.0717 (Ian G. Moss)

BRST-invariant boundary conditions and strong ellipticity    [PDF]

Ian G. Moss

The quantisation of gauge theories usually proceedes through the introduction of ghost fields and BRST symmetry. A long-standing issue for quantum gauge theory in the presence of boundaries has been the fact that BRST-invariant boundary value problems for the gauge field operators can be non-elliptic, and 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, but which are non-elliptic. This prompts a discussion of the wider issue of non-ellipticity in BRST-invariant boundary value problems and leads to a method for constructing the heat kernel for these boundary-value problems.

View original: http://arxiv.org/abs/1301.0717