2 research outputs found
Fluctuations of quantum fields via zeta function regularization
Explicit expressions for the expectation values and the variances of some
observables, which are bilinear quantities in the quantum fields on a
D-dimensional manifold, are derived making use of zeta function regularization.
It is found that the variance, related to the second functional variation of
the effective action, requires a further regularization and that the relative
regularized variance turns out to be 2/N, where N is the number of the fields,
thus being independent on the dimension D. Some illustrating examples are
worked through.Comment: 15 pages, latex, typographical mistakes correcte
Quantum Scalar Field on the Massless (2+1)-Dimensional Black Hole Background
The behavior of a quantum scalar field is studied in the metric ground state
of the (2+1)-dimensional black hole of Ba\~nados, Teitelboim and Zanelli which
contains a naked singularity. The one-loop BTZ partition function and the
associate black hole effective entropy, the expectation value of the quantum
fluctuation as well as the renormalized expectation value of the stress tensor
are explicitly computed in the framework of the -function procedure.
This is done for all values of the coupling with the curvature, the mass of the
field and the temperature of the quantum state. In the massless conformally
coupled case, the found stress tensor is used for determining the quantum back
reaction on the metric due to the scalar field in the quantum vacuum state, by
solving the semiclassical Einstein equations. It is finally argued that, within
the framework of the 1/N expansion, the Cosmic Censorship Hypothesis is
implemented since the naked singularity of the ground state metric is shielded
by an event horizon created by the back reaction.Comment: 18 pages, RevTeX, no figures, minor changes, final version accepted
for publication in Phys. Rev.