arXiv subjects

G. A. Vilkovisky

Publications and source records attributed to G. A. Vilkovisky.

17 recordsLinked to original sources

arXiv2009

Covariant Perturbation Theory (IV). Third Order in the Curvature

The trace of the heat kernel and the one-loop effective action for the generic differential operator are calculated to third order in the background curvatures: the Riemann curvature, the commutator curvature and the potential. In the case of effective action, this is equivalent to a calculation (in the covariant form) of the one-loop vertices in all models of gravitating fields. The basis of nonlocal invariants of third order in the curvature is built, and constraints arising between these invariants in low-dimensional manifolds are obtained. All third-order form factors in the heat kernel and effective action are calculated, and several integral representations for them are obtained. In the case of effective action, this includes a specially generalized spectral representation used in applications to the expectation-value equations. The results for the heat kernel are checked by deriving all the known coefficients of the Schwinger-DeWitt expansion including $a_3$ and the cubic terms of $a_4$. The results for the effective action are checked by deriving the trace anomaly in two and four dimensions. In four dimensions, this derivation is carried out by several different techniques elucidating the mechanism by which the local anomaly emerges from the nonlocal action. In two dimensions, it is shown by a direct calculation that the series for the effective action terminates at second order in the curvature. The asymptotic behaviours of the form factors are calculated including the late-time behaviour in the heat kernel and the small-$\Box$ behaviour in the effective action. In quantum gravity, the latter behaviour contains the effects of vacuum radiation including the Hawking effect.

hep-th↗

arXiv2008

Post-radiation evolution of black holes

The expectation-value equations for the collapse of a macroscopic, spherically symmetric, and uncharged body are integrated up to the limit of validity of semiclassical theory. The collapse finishes with a true stable black hole of the mass microscopically exceeding the vacuum-induced charge. The apparent horizon is almost closed. The most important feature of the solution is the presence of an irremovable Cauchy horizon.

hep-th↗

arXiv2007

Expectation values and vacuum currents of quantum fields

Theory of expectation values is presented as an alternative to S-matrix theory for quantum fields. This change of emphasis is conditioned by a transition from the accelerator physics to astrophysics and cosmology. The issues discussed are the time-loop formalism, the Schwinger - Keldysh diagrams, the effective action, the vacuum currents, and the effect of particle creation.

hep-th↗

arXiv2005

Kinematics of evaporating black holes

The correspondence principle and causality divide the spacetime of a macroscopic collapsing mass into three regions: classical, semiclassical, and ultraviolet. The semiclassical region covers the entire evolution of the black hole from the macroscopic to the microscopic scale if the latter is reached. It is shown that the metric in the semiclassical region is expressed purely kinematically through the Bondi charges. The only quantum calculation needed is the one of radiation at infinity. The ultraviolet ignorance of semiclassical theory is irrelevant. The metric with arbitrary Bondi charges is obtained and studied.

hep-th↗

arXiv2005

Radiation equations for black holes

It has been shown in the previous paper that the metric in the semiclassical region of the collapse spacetime is expressed purely kinematically through the Bondi charges. Here the Bondi charges are expressed through this metric by calculating the vacuum radiation against its background. The result is closed equations for the metric and the Bondi charges. Notably, there is a nonvanishing flux of the vacuum-induced matter charge.

hep-th↗

arXiv2005

Backreaction of the Hawking radiation

Black holes create a vacuum matter charge to protect themselves from the quantum evaporation. A spherically symmetric black hole having initially no matter charges radiates away about 10% of the initial mass and comes to a state in which the vacuum-induced charge equals the remaining mass.

hep-th↗

arXiv2000

On electrodynamics of rapidly moving sources

Rapidly moving sources create pairs in the vacuum and lose energy. In consequence of this, the velocity of a charged body cannot approach the speed of light closer than a certain limit which depends only on the coupling constant. The vacuum back-reaction secures the observance of the conservation laws. A source can lose up to 50% of energy and charge because of the vacuum instability.

hep-th↗

arXiv1999

The vacuum backreaction on a pair creating source

Solution is presented to the simplest problem about the vacuum backreaction on a pair creating source. The backreaction effect is nonanalytic in the coupling constant and restores completely the energy conservation law. The vacuum changes the kinematics of motion like relativity theory does and imposes a new upper bound on the velocity of the source.

hep-th↗

arXiv1999

Master equation in the general gauge: on the problem of infinite reducibility

The master equation is quantized. This is an example of quantization of a gauge theory with nilpotent generators. No ghosts are needed for a generation of the gauge algebra. The point about the nilpotent generators is that one can't write down a single functional integral for this theory. One has to write down a product of two coupled functional integrals and take a square root. In the special gauge where the gauge conditions are commuting, the functional integrals decouple, and one recovers the known result.

hep-th↗

arXiv1998

Vacuum amplification of the high-frequency electromagnetic radiation

When an electrically charged source is capable of both emitting the electromagnetic waves and creating charged particles from the vacuum, its radiation gets so much amplified that only the backreaction of the vacuum makes it finite. The released energy and charge are calculated in the high-frequency approximation. The technique of expectation values is advanced and employed.

hep-th↗

arXiv1998

Particle creation in the effective action method

The effect of particle creation by nonstationary external fields is considered as a radiation effect in the expectation-value spacetime. The energy of created massless particles is calculated as the vacuum contribution in the energy-momentum tensor of the expectation value of the metric. The calculation is carried out for an arbitrary quantum field coupled to all external fields entering the general second-order equation. The result is obtained as a functional of the external fields. The paper gives a systematic derivation of this result on the basis of the nonlocal effective action. Although the derivation is quite involved and touches on many aspects of the theory, the result itself is remarkably simple. It brings the quantum problem of particle creation to the level of complexity of the classical radiation problem. For external fields like the electromagnetic or gravitational field there appears a quantity, the radiation moment, that governs both the classical radiation of waves and the quantum particle production. The vacuum radiation of an electrically charged source is considered as an example. The research is aimed at the problem of backreaction of the vacuum radiation.

gr-qc↗

arXiv1995

Partial summation of the nonlocal expansion for the gravitational effective action in 4 dimensions

The vacuum action for the gravitational field admits a known expansion in powers of the Ricci tensor with nonlocal operator coefficients (form factors). We show that going over to a different basis of curvature invariants makes possible a partial summation of this expansion. Only the form factors of the Weyl-tensor invariants need be calculated. The full action is then uniquely recovered to all orders from the knowledge of the trace anomaly. We present an explicit expression for the partially summed action, and point out simplifications resulting in the vertex functions. An application to the effect of the vacuum gravitational waves is discussed.

hep-th↗

arXiv1995

The one-loop form factors in the effective action, and production of coherent gravitons from the vacuum

We present the solution of the problem of the $1/\Box, \Box \to 0,$ asymptotic terms discovered in the one-loop form factors of the gravitational effective action. Owing to certain constraints among their coefficients, which we establish, these terms cancel in the vacuum stress tensor and do not violate the asymptotic flatness of the expectation value of the metric. They reappear, however, in the Riemann tensor of this metric and stand for a new effect: a radiation of gravitational waves induced by the vacuum stress. This coherent radiation caused by the backreaction adds to the noncoherent radiation caused by the pair creation in the case where the initial state provides the vacuum stress tensor with a quadrupole moment.

hep-th↗

arXiv1994

The one-loop effective action and trace anomaly in four dimensions

The one-loop effective action for a generic set of quantum fields is calculared as a nonlocal expansion in powers of the curvatures (field strengths). This expansion is obtained to third order in the curvature. It is stressed that the covariant vertices are finite. The trace anomaly in four dimensions is obtained directly by varying the effective action. The nonlocal terms in the action, producing the anomaly, contain non-trivial functions of three operator arguments. The trace anomaly is derived also by making the conformal transformation in the heat kernel.

hep-th↗

arXiv1994

The basis of nonlocal curvature invariants in quantum gravity theory

A complete basis of nonlocal invariants in quantum gravity theory is built to third order in spacetime curvature and matter-field strengths. The nonlocal identities are obtained which reduce this basis for manifolds with dimensionality $2ω<6$. The present results are used in heat-kernel theory, theory of gauge fields and serve as a basis for the model-independent approach to quantum gravity and, in particular, for the study of nonlocal vacuum effects in the gravitational collapse problem.

gr-qc↗

arXiv1994

Asymptotic behaviours of the heat kernel in covariant perturbation theory

The trace of the heat kernel is expanded in a basis of nonlocal curvature invariants of $N$th order. The coefficients of this expansion (the nonlocal form factors) are calculated to third order in the curvature inclusive. The early-time and late-time asymptotic behaviours of the trace of the heat kernel are presented with this accuracy. The late-time behaviour gives the criterion of analyticity of the effective action in quantum field theory. The latter point is exemplified by deriving the effective action in two dimensions.

gr-qc↗

arXiv1993

Planckian Energy Scattering and Surface Terms in the Gravitational Action

This is a revised version of our previous paper by the same name and preprint number. It contains various changes, two figures and new results in sect.5. We propose a new approach to four-dimensional Planckian-energy scattering in which the phase of the ${\cal S}$-matrix is written---to leading order in $\hbar$ and to all orders in $R/b =Gs/J$---in terms of the surface term of the gravity action and of a boundary term for the colliding quanta. The proposal is checked at the leading order in $R/b$ and also against some known examples of scattering in strong gravitational fields.

hep-th↗