214 research outputs found
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
Nonassociative Weyl star products
Deformation quantization is a formal deformation of the algebra of smooth
functions on some manifold. In the classical setting, the Poisson bracket
serves as an initial conditions, while the associativity allows to proceed to
higher orders. Some applications to string theory require deformation in the
direction of a quasi-Poisson bracket (that does not satisfy the Jacobi
identity). This initial condition is incompatible with associativity, it is
quite unclear which restrictions can be imposed on the deformation. We show
that for any quasi-Poisson bracket the deformation quantization exists and is
essentially unique if one requires (weak) hermiticity and the Weyl condition.
We also propose an iterative procedure that allows to compute the star product
up to any desired order.Comment: discussion extended, tipos corrected, published versio
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
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