The Faddeev-Popov trick in the presence of boundaries

We formulate criteria of applicability of the Faddeev-Popov trick to gauge theories on manifolds with boundaries. With the example of Euclidean Maxwell theory we demonstrate that the path integral is indeed gauge independent when these criteria are satisfied, and depends on a gauge choice whenever these criteria are violated. In the latter case gauge dependent boundary conditions are required for a self-consistent formulation of the path intgral.Comment: LaTEX, 10p

Comment on gauge choices and physical variables in QED

We consider possible definitions of physical variables in QED. We demonstrate that the condition $\partial_i A_i$$=0$ is the most convenient one because it leads to path integral over physical components with local action. However, other choices, as $A_3=0$, are also possible. The standard expression for configuration space path integral in $A_3=0$ gauge is obtained starting with reduced phase space formulation. Contrary to the claims of the paper [M.Lavelle and D.McMullan,Phys. Lett. B316 (1993)172] the $A_3=0$ gauge is not overconstrained.Comment: 4 pages, SPbU-IP-94-8, Late

Parity anomaly in four dimensions

In an analogy to the odd-dimensional case we define the parity anomaly as the part of the one-loop effective action for fermions associated with spectral asymmetry of the Dirac operator. This quantity is computed directly on four-dimensional manifolds with boundary and related to the Chern-Simons current on the boundary. Despite a quite unusual Chern-Simons level obtained, the action is gauge invariant and passes all consistency checks.Comment: Revtex, 7 pp V2: added remarks and reference

Hawking radiation from dilaton gravity in 1 + 1 dimensions: a pedagogical review

Hawking radiation in d=4 is regarded as a well understood quantum theoretical feature of Black Holes or of other geometric backgrounds with an event horizon. On the other hand, the dilaton theory emerging after spherical reduction and generalized dilaton theories only during the last years became the subject of numerous studies which unveiled a surprisingly difficult situation. Recently we have found some solution to the problem of Hawking flux in spherically reduced gravity which has the merit of using a minimal input. It leads to exact cancellation of negative contributions to this radiative flux, encountered in other approaches at infinity, so that our result asymptotically coincides with the one of minimally coupled scalars. The use of an integrated action is avoided - although we have been able to present also that quantity in a closed expression. This short review also summarizes and critically discusses recent activities in this field, including the problem of ``conformal frames'' for the background and questions which seem to be open in our own approach as well as in others.Comment: latex2e, to appear in Annalen der Physi

Reduced phase space quantization of Ashtekar's gravity on de Sitter background

We solve perturbative constraints and eliminate gauge freedom for Ashtekar's gravity on de Sitter background. We show that the reduced phase space consists of transverse, traceless, symmetric fluctuations of the triad and of transverse, traceless, symmetric fluctuations of the connection. A part of gauge freedom corresponding to the conformal Killing vectors of the three-manifold can be fixed only by imposing conditions on Lagrange multiplier. The reduced phase space is equivalent to that of ADM gravity on the same background.Comment: 9, CEBAF-TH-94-0