S. A. Fulling

Radiation from a moving mirror in two dimensional space-time: conformal anomaly

The energy-momentum tensor is calculated in the two dimensional quantum theory of a massless scalar field influenced by the motion of a perfectly reflecting boundary (mirror). This simple model system evidently can provide insight into more sophisticated processes, such as particle production in cosmological models and exploding black holes. In spite of the conformally static nature of the problem, the vacuum expectation value of the tensor for an arbitrary mirror trajectory exhibits a non-vanishing radiation flux (which may be readily computed). The expectation value of the instantaneous energy flux is negative when the proper acceleration of the mirror is increasing, but the total energy radiated during a bounded mirror motion is positive. A uniformly accelerating mirror does not radiate; however, our quantization does not coincide with the treatment of that system as a ‘static universe’. The calculation of the expectation value requires a regularization procedure of covariant separation of points (in products of field operators) along time-like geodesics; more naïve methods do not yield the same answers. A striking example involving two mirrors clarifies the significance of the conformal anomaly.

Singularity structure of the two-point function in quantum field theory in curved spacetime, II

Abstract We prove that, for a massive, scalar, quantum field in a wide class of static spacetimes, the two-point function 〈0|φ( x ) φ( y ) + φ( y ) φ( x )|0〉 has singularity structure of the Hadamard form. In particular, this implies that the point-splitting renormalization prescription is well defined in these spacetimes. As a corollary of this result and a previous result of Fulling. Sweeny, and Wald, we show that in an arbitrary globally hyperbolic spacetime there always exists a large class of states for which the singular part of the two-point function has the Hadamard form. In addition, we prove that, for a closed universe which is both initially and finally static, the S-matrix exists.

Exponential decay of energy of evolution equations with locally distributed damping

Consider an evolution equation with energy dissipation, \[ \frac{\partial }{{\partial t}}y( {x,t} ) = Ay( {x,t} ) + By( {x,t} ) \] on a bounded x-domain

Singularity structure of the two-point function quantum field theory in curved spacetime

\Omega

Radiation from Moving Mirrors and from Black Holes

, where

Temperature, periodicity and horizons

By

REMARKS ON POSITIVE FREQUENCY AND HAMILTONIANS IN EXPANDING UNIVERSES

signifies a dissipative perturbation to an otherwise energy-conserving system. This dissipation may be due to medium impurities, viscous effects, or artificially imposed dampers and stabilizers. It is distributed over only part of the domain

Energy-momentum tensor of a massless scalar quantum field in a Robertson-Walker universe

\Omega

Systematics of the relationship between vacuum energy calculations and heat-kernel coefficients

. The question of when the dissipation is effective enough to cause uniform exponential decay of energy is examined.Because of the locally distributed nature of energy dissipation, the problem lacks coercivity and is not directly solvable by energy identities. Thus, to get conditions sufficient for uniform exponential decay, a different approach needs to be taken. Provided here is a set of tight sufficient conditions in terms of the influence of the dissipative operatorBon the separated eigenmodes or clustered eigenmodes ofA. The main theorems are general enough to treat the wave and bea...

How Does Casimir Energy Fall

In the point-splitting prescription for renormalizing the stress-energy tensor of a scalar field in curved spacetime, it is assumed that the anticommutator expectation valueG(x, x′)=〈ø(x)ø(x′)+ø(x′)ø(x)〉 has a singularity of the Hadamard form asx→x′. We prove here that ifG(x,x′) has the Hadamard singularity structure in an open neighborhood of a Cauchy surface, then it does so everywhere, i.e., Cauchy evolution preserves the Hadamard singularity structure. In particular, in a spacetime which is flat below a Cauchy surface, for the “in” vacuum stateG(x,x′) is of the Hadamard form everywhere, and thus the point-splitting prescription in this case has been rigorously shown to give meaningful, finite answers.