Gluon field strength correlation functions within a constrained instanton model

We suggest a constrained instanton (CI) solution in the physical QCD vacuum which is described by large-scale vacuum field fluctuations. This solution decays exponentially at large distances. It is stable only if the interaction of the instanton with the background vacuum field is small and additional constraints are introduced. The CI solution is explicitly constructed in the ansatz form, and the two-point vacuum correlator of the gluon field strengths is calculated in the framework of the effective instanton vacuum model. At small distances the results are qualitatively similar to the single instanton case; in particular, the invariant structure is small, which is in agreement with the lattice calculations. Received: 18 June 1999 / Revised version: 21 July 1999 / Published online: 17 February 2000     

Colliding Plane Waves in Einstein–Maxwell Theory

Recently, a simple solution of the vacuum Einstein–Maxwell field equations was given describing a plane electromagnetic shock wave sharing its wave front with a plane gravitational impulse wave. We present here an exact solution of the vacuum Einstein–Maxwell field equations describing the head-on collision of such a wave with a plane gravitational impulse wave. The solution has the Penrose–Khan solution and a solution obtained by Griffiths as separate limiting cases.     

Weakened field equations in General Relativity admitting an ‘unphysical’ metric

Certain weakened vacuum field equations which have been suggested as alternatives to the vacuum field equations of General Relativity are investigated. It is shown that they each possess a solution which corresponds to an isolated mass at the origin which repels test particles. In view of the contradiction with experiment this solution is an embarrassment to these proposed vacuum field equations.On leave of absence from the Department of Mathematics, The University, Bristol.     

Singularity-free model of electric charge in physical vacuum: non-zero spatial extent and mass generation

We propose a model of a spinless electrical charge as a self-consistent field configuration of the electromagnetic (EM) field interacting with a physical vacuum effectively described by the logarithmic quantum Bose liquid. We show that, in contrast to the EM field propagating in a trivial vacuum, a regular solution does exist, and both its mass and spatial extent emerge naturally from dynamics. It is demonstrated that the charge and energy density distribution acquire Gaussian-like form. The solution in the logarithmic model is stable and energetically favourable, unlike that obtained in a model with a quartic (Higgs-like) potential.     

Generalized Vaidya metrics

We investigate criteria under which one may construct the energy tensor of a null radiation field from an algebraically special vacuum metric. The field bears the same relationship to the original metric as does Vaidya's to Schwarzschild's. As an example we generate a class of null radiation fields from a class of vacuum metrics without symmetry discovered by Robinson and Robinson.Supported in part by the National Science Foundation (GP-8868, GP-20033, and GU-1598), Air Force Office of Scientific Research under Grant AF-AFOSR-903-67 and by the National Aeronautics and Space Administration under NASA Grant No. NGL 44-004-001.     

A family of Jordan-Brans-Dicke Kerr solutions

A family of solutions of the vacuum Jordan-Brans-Dicke or scalar-tensor gravitational field equations is given. This family reduces to the Kerr rotating solution of the vacuum Einstein equations when the scalar field is constant. The family does not have spherical symmetry when the rotation is zero and the scalar field is not constant. The method used to generate the new solutions can also be used to obtain vacuum Jordan-Brans-Dicke solutions from any given vacuum stationary, axisymmetric solution.     

New exact solutions of Einstein's field equations: Gravitational force can also be repulsive!

This article has not been written for specialists of exact solutions of Einstein's field equations but for physicists who are interested in nontrivial information on this topic. We recall the history and some basic properties of exact solutions of Einstein's vacuum equations. We show that the field equations for stationary axisymmetric vacuum gravitational fields can be expressed by only one nonlinear differential equation for a complex function. This compact form of the field equations allows the generation of almost all stationary axisymmetric vacuum gravitational fields. We present a new stationary two-body solution of Einstein's equations as an application of this generation technique. This new solution proves the existence of a macroscopic, repulsive spin-spin interaction in general relativity. Some estimates that are related to this new two-body solution are given.     

Spherically Symmetric Vacuum Brane and Wormhole Solutions

In this letter, we have obtained static, spherically symmetric solutions of the effective vacuum Einstein field equations on a brane embedded in a five dimensional space time. The effective stress tensor is induced by the interaction with the bulk gravitational field and is given by the electric part of the five dimensional Weyl tensor. Due to traceless nature of this non-local effect of the bulk, any solution of  ⁽⁴⁾ R=0 is a possible solution of the vacuum brane. We have derived a class of solutions, which corresponds to wormhole solution. Physical properties and characteristics of the wormhole are studied.     

Stationary vacuum fields with cylindrical symmetry

It is demonstrated that a stationary vacuum field solution with cylindrical symmetry is always reducible to a static cylindrically symmetric solution.     

Black hole in a gravitational field

An exact solution of the vacuum Einstein field equations representing a Schwarzschild black hole in an external gravitational field is derived using a formalism developed by Ernst.     

Boosted cylindrical magnetized Kaluza–Klein wormhole

In this work, we consider a vacuum solution of Kaluza–Klein theory with cylindrical symmetry. We investigate the physical properties of the solution as viewed in four dimensional spacetime, which turns out to be a stationary, cylindrical wormhole supported by a scalar field and a magnetic field oriented along the wormhole. We then apply a boost to the five dimensional solution along the extra dimension, and perform the Kaluza–Klein reduction. As a result, we show that the new solution is still a wormhole with a radial electric field and a magnetic field stretched along the wormhole throat.     

Reggeon field with non-vanishing vacuum expectation value

It is argued that if the vacuum expectation value of the reggeon field does not vanish, the solution of the reggeon calculus corresponds to the leading singularity of intercept one. The physical interpretation of the reggeon field theory with unstable vacuum is discussed.     

The gravitational field of a nullicle

We present a natural generalization of the Schwarzschild solution. It is an exact solution of the vacuum Einstein field equations and is interpreted as the gravitational field of a nullicle (null-particle).     

Radiation reaction

I solve Maxwell's equation for a current produced by a classical, point electron. My solution, which represents the self electromagnetic field of the electron, can be found along the electron trajectory, where the conventional retarded-time solution is singular. The solution is in the form of an integral over all spectral frequencies of the field and has an Ehrenfest correspondence with the operator field of quantum electrodynamics (QED). Use of the field in the equation of motion for a harmonically-bound electron leads to an equation having the same form as the Schrödinger equation for a two-level atom interacting with the QED vacuum field.     

强场下真空中粒子对产生的研究进展

随着激光技术的飞快发展,激光强度不断提高,超强外场下真空中正负电子对产生的过程,即能量向质量转化过程,已经成为一个研究热点。主要综述了近几年量子Vlasov方程方法和计算量子场论(数值求解Dirac方程)方法在研究强场下真空中正负电子对产生方面的进展,分别介绍了空间均匀场和空间不均匀场下的粒子对产生的情况。第一种情况主要介绍双脉冲结构振荡电场中电子-正电子对的产生、强双频振荡电场中非微扰电子-正电子对的产生、频率调制的激光场中电子-正电子对的产生和Dirac真空对啁啾外场的快速分辨。第二种情况主要介绍优化空间局域电场提高粒子对的产生率、多个势阱-垒结构的振荡场对粒子对产生的增强、振荡 Sauter 电势中正负电子对产生的问题、操纵Dirac真空以控制其在场诱导下的衰变、作为信息传输介质的Dirac真空还有正负电子对产生中的相干和非相干啁啾机制的转变。     

The zero momentum limit of the vacuum polarization at finite temperature

We examine the zero momentum limit of the finite temperature vacuum polarization for a quantized scalar field coupled to a classical external field. Ordinarily, this type of Feynman diagram is plagued by nonanalytic behaviour when the external momentum tends to zero. Using imaginary-time, we show that this behaviour is not present in an exact background field solution and how the Feynman diagram calculation may be trivially modified to match the exact solution. Comparisons with recent real-time results are also made.     

Solitonic Information Transmission in General Relativity

An exact solution of the vacuum Einstein＇s field equations is presented, in which there exists a congruence of null geodesics whose shear behaves like a travelling wave of the KdV equation. On the basis of this exact solution, the feasibility of solitonic information transmission by exploiting the nonlinearity intrinsic to the Einstein field equations is discussed.     

Axisymmetric vacuum fields in general projective relativity

A method has been derived which enables one to obtain solutions to the stationary, axially symmetric vacuum fields in general projective relativity developed by Arcidiacono from known solutions of the vacuum field in Einstein's theory. The analogue of the Kerr solution in general projective relativity has been obtained as an example. Finally, a relation between the stationary and static axially symmetric vacuum fields in general projective relativity has been derived.     

On the sources of static plane symmetric vacuum space-times

The sources of static vacuum plane space-times with reflection symmetry are considered. It is argued that the counterpart of the Einstein theory to the gravitational field of a massive Newtonian plane should be described by the Rindler solution, which represents also a uniform gravitational field, and the test particles moving in which have constant accelerations.