Calculation of an effective potential in an external gravitational field with torsion and phase transitions induced by external fields

We find a general expression for a one-loop effective potential of an arbitrary massless theory with accuracy up to terms linear in two-dimensional invariants. The potential is constructed from the metric and the torsion. We show that spontaneous symmetry breaking can occur in the form of a first-order phase transition induced jointly by the curvature and the torsion.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 3–9, March, 1987.The authors are grateful to I. V. Tyutin and E. S. Fradkin for discussion.     

Behavior of effective charges in a quantum-field-theory model in an external gravitational field with torsion

Renormalization group equations are obtained for the parameters of nonminimal coupling of matter with an external gravitational field with torsion. The asymptotical behavior of these parameters in the short-distance limit is studied. The asymptotical conformal invariance of the theory is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 58–62, December, 1985.     

Expulsion of external fields from extreme horizons: Example of an external gravitational field

In analogy with the Meissner effect in (super) conductors, black holes expel stationary axisymmetric external fields when approaching the extreme state. This has been studied on magnetic fields in the literature. Using the recently obtained solution describing a rotating black hole surrounded by an axisymmetric thin annular disc, we show that the effect also applies to an external gravitational field. This note on “traditional” Prague subject is dedicated to Professor Jiří Bičák on the occasion of his 60th birthday.     

Electrostatic potential in a gravitational field

The electrostatic potential in a gravitational field is estimated up to the order ofe ² G ² in the framework of the conventional quantum field theory. It is shown that the electrostatic potential is different from the classical one. We find that this discrepancy is attributable to the process in which a particle emits three massless ones which are absorbed by three other particles.     

Weak gravitational field and Coriolis potential

In mechanics of the mass point passage from one frame of reference to another moving with velocity consists in subtracting this vector from the velocity of the particle. In general case the vector is not constant, as, for example, when passing through a rotating frame, this operation creates inertial forces. Analysis of this phenomenon from the point of view of Lagrangian and Hamiltonian mechanics is interesting from the general relativistic point of view due to Einstein’s principle of equivalence. We show that the vector plays the role of vector potential which, however, essentially differs from vector potential known in classical electrodynamics. Comparative analysis of the two kinds of vector potentials is completed.      

An exact solution of Einstein's equations for two particles falling freely in an external gravitational field

I begin with a Weyl axially symmetric, static metric representing a spherical particle in equilibrium under the attraction of a semi-infinite rod (s.i.r.) of line density 1/2 and another, pseudo-uniform, gravitational field. A coordinate transformation is then used to remove the s.i.r., enlarge the spacetime, and make the solution time-dependent. The result represents two spherical particles (which do not interact because each is outside the null cone of the other) moving in a certain gravitational wave field. It is shown that the particles move on geodesies of the background wave field. The sources of the wave field are briefly investigated.     

Induction of the gravitational constant in an electric field

We investigate the induction of the gravitational constant by a complex scalar field in curved space with the help of the spontaneous symmetry breaking effect. It is shown that the presence of a periodic electric field induces small variations in the Newtonian gravitational constant.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 98–102, April, 1989.In conclusion, the author expresses thanks to the participants in Professor A. A. Grib's seminar for useful discussions.     

Local momentum-space representation of graviton propagators in an external gravitational field and one-loop counterterms in quantum gravity

Local momentum-space representation of graviton and ghost propagators in an arbitrary external gravitational field is constructed. It is shown that this representation allows to easily obtain one-loop counterterms in quantum gravity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 50–53, April, 1984.     

Velocity of a signal in an attractive potential and propagation of light in a gravitational field

The propagation of a massless field in attractive and repulsive potentials is considered. It is shown that though the group velocity in such potentials can be larger than one, the wave front propagates with the speed of light. A larger-than-one group velocity leads only to a strong deformation of the wave packet. The results obtained are applied to the light propagation in a gravitational field. An erroneous assertion concerning the last problem, recently made in the literature, is refuted.     

具有广义协变的包含重力场贡献的重力场方程

利用半度规λ^(α)_μ表象的数学工具定义一个对广义坐标具有协变形式的重力场矢势函数ω^(α)_μ≡-cλ^(α)_μ，给出一个具有广义协变的包含重力场贡献的重力场方程R_μν-g_μνR/2+Λg_μν=8πG(T^(Ⅰ)_μν+T^(Ⅱ)_μν) 关键词： 重力场方程 协变形式 能量-动量张量 量子化     

Wigner's pseudo-particle relativistic dynamics in external potential field

The Wigner's pseudo-particle formalism has been generalized to describe quantum dynamics of relativistic particle in external potential field. As a simplest application of the developed formalism the time evolution of the 1D relativistic quantum harmonic oscillator been considered. Due to the complex structure of the evolution equation for Wigner function, the only numerical treatment is possible by combining Monte Carlo and molecular dynamics methods. Relativistic dynamics results in appearance of the new physical effects as opposed to non-relativistic case. Interesting is the complete changing of the shape of the momentum and coordinate distribution functions as well as formation of ‘unexpected’ protuberances. To analyze the influence of relativistic effects on average values of quantum operators, the dependencies on time of average momentum, position, their dispersions and energy have been compared for the non-relativistic and relativistic dynamics.     

On the gravitational field acting as an optical medium

Given a curved space-time with a metric tensorg _ij, Maxwell's equations may be written as if they were valid in a flat space-time in which there is an optical medium with a constitutive equation.When optical phenomena are considered, this medium turns out to be equivalent to the gravitational field. Optical phenomena in various gravitational fields are analysed and we find that the language of classical optics for the equivalent medium is as suitable as that of Riemannian geometry.This work was started at the Department of Applied Mathematics and Theoretical Physics, Cambridge, England.     

Neutrino transitions in an external field

In the article the transitionv _e f v is considered in a field of plane-wave type, induced by the effective values of the anomalous magnetic and electric dipole moments of massive neutrinos. The possible contribution of the given mechanism to the background of quantum mechanical oscillatory phenomena is discussed.Moscow State Correspondence Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 31–35, January, 1993.     

Magnetic fluids in an external field

Within mean field approximation we investigate the phase diagrams of magnetic fluids in presence of a magnetic field. In a finite field the magnetic phase transition is absent, but instead a line of first order liquid-liquid transitions ending in a critical point occurs for a magnetic interaction, which is sufficiently strong. Varying the magnetic field these critical points extend from the tricritical point at H=0 to a critical endpoint. For a fluid with Ising spins we calculate the critical lines and several tricritical exponents analytically. For Heisenberg fluids we obtain the phase diagrams from a numerical solution of the mean field equations of state. Received 20 March 1998     

The potential of effective field theory in NN scattering

We study an effective field theory of interacting nucleons at distances much greater than the pion's Compton wavelength. In this regime the NN potential is conjectured to be the sum of a delta function and its derivatives. The question we address is whether this sum can be consistently truncated at a given order in the derivative expansion, and systematically improved by going to higher orders. Regularizing the Lippmann-Schwinger equation using a cutoff we find that the cutoff can be taken to infinity only if the effective range is negative. A positive effective range — which occurs in nature — requires that the cutoff be kept finite and below the scale of the physics which has been integrated out, i.e. O(m_π). Comparison of cutoff schemes and dimensional regularization reveals that the physical scattering amplitude is sensitive to the choice of regulator. Moreover, we show that the presence of some regulator scale, a feature absent in dimensional regularization, is essential if the effective field theory of NN scattering is to be useful. We also show that one can define a procedure where finite cutoff dependence in the scattering amplitude is removed order by order in the effective potential. However, the characteristic momentum in the problem is given by the cutoff, and not by the external momentum. It follows that in the presence of a finite cutoff there is no small parameter in the effective potential, and consequently no systematic truncation of the derivative expansion can be made. We conclude that there is no effective field theory of NN scattering with nucleons alone.     

Renormalization of QED in an external field

The Schwinger equations of QED are rewritten in three different ways as integral equations involving functional derivatives, which are called weak field, strong field, and SCF quantum electrodynamics. The perturbative solutions of these equations are given in terms of appropriate Feynman diagrams. The Green function that is used as an electron propagator in each case is discussed in detail. The general renormalization rules for each of the three equations are provided both in a non perturbative way (Dyson relations) and for Feynman diagrams.