51 research outputs found
Energy-Momentum Tensor and Particle Creation in the de Sitter Universe
For a quantum field in a curved background the choice of the vacuum state is
crucial. We exhibit a vacuum state in which the expectation values of the
energy and pressure allow an intuitive interpretation. We apply this general
result to the de Sitter universe.Comment: 3 pages, 1 figure, revtex. To appear in the proceedings of the 8th
Marcel Grossmann Meetin
Quantum Gravity Without Ghosts
An outline is given of a recently discovered technique for building a quantum
effective action that is completely independent of gauge-fixing choices and
ghost determinants. One makes maximum use of the geometry and fibre-bundle
structure of the space of field histories and introduces a set of nonlocal
composite fields: the geodesic normal fields based on Vilkovisky's connection
on the space of histories. The closed-time-path formalism of Schwinger, Bakshi,
Mahantappa {\it et al} can be adapted for these fields, and a set of
gauge-fixing-independent dynamical equations for their expectation values
(starting from given initial conditions) can be computed. An obvious
application for such equations is to the study of the formation and radiative
decay of black holes, and to other back-reaction problems.Comment: This is a paper submitted to the Gravity Research Foundation Essay
Competition of 1998 that received Honorable Mentio
Large Scale Features of Rotating Forced Turbulence
Large scale features of a randomly isotropically forced incompressible and
unbounded rotating fluid are examined in perturbation theory. At first order in
both the random force amplitude and the angular velocity we find two types of
modifications to the fluid equation of motion. The first correction transforms
the molecular shear viscosity into a (rotation independent) effective
viscosity. The second perturbative correction leads to a new large scale
non-dissipative force proportional to the fluid angular velocity in the slow
rotation regime. This effective force does no net work and alters the
dispersion relation of inertial waves propagating in the fluid. Both
dynamically generated corrections can be identified with certain components of
the most general axisymmetric ``viscosity tensor'' for a Newtonian fluid.Comment: 12 pages, 2 figures, RevTeX, and accepted for publication in Phys.
Rev.
Cosmological Horizon Modes and Linear Response in de Sitter Spacetime
Linearized fluctuations of quantized matter fields and the spacetime geometry
around de Sitter space are considered in the case that the matter fields are
conformally invariant. Taking the unperturbed state of the matter to be the de
Sitter invariant Bunch-Davies state, the linear variation of the stress tensor
about its self-consistent mean value serves as a source for fluctuations in the
geometry through the semi-classical Einstein equations. This linear response
framework is used to investigate both the importance of quantum backreaction
and the validity of the semi-classical approximation in cosmology. The full
variation of the stress tensor, delta T^a_b contains two kinds of terms: (1)
those that depend explicitly upon the linearized metric variation delta g_{cd}
through the [T^a_b, T^{cd}] causal response function; and (2) state dependent
variations, independent of delta g_{cd}. For perturbations of the first kind,
the criterion for the validity of the semi-classical approximation in de Sitter
space is satisfied for fluctuations on all scales well below the Planck scale.
The perturbations of the second kind contain additional massless scalar degrees
of freedom associated with changes of state of the fields on the cosmological
horizon scale. These scalar degrees of freedom arise necessarily from the local
auxiliary field form of the effective action associated with the trace anomaly,
are potentially large on the horizon scale, and therefore can lead to
substantial non-linear quantum backreaction effects in cosmology.Comment: 62 pages, 4 figures v.2 is amended to match the published version in
Phys. Rev. D: Eqs. (6.13)-(6.14) for the quadratic action added, two
references added, several minor typos correcte
Renormalization Group Improving the Effective Action
The existence of fluctuations together with interactions leads to
scale-dependence in the couplings of quantum field theories for the case of
quantum fluctuations, and in the couplings of stochastic systems when the
fluctuations are of thermal or statistical nature. In both cases the effects of
these fluctuations can be accounted for by solutions of the corresponding
renormalization group equations. We show how the renormalization group
equations are intimately connected with the effective action: given the
effective action we can extract the renormalization group equations; given the
renormalization group equations the effects of these fluctuations can be
included in the classical action by using what is known as improved
perturbation theory (wherein the bare parameters appearing in tree-level
expressions are replaced by their scale-dependent running forms). The improved
action can then be used to reconstruct the effective action, up to finite
renormalizations, and gradient terms.Comment: 25 pages, ReV-TeX 3.
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