On the Goldstonic gravitation theory

The physical specificity of gravity as a Goldstone-type field responsible for spontaneous breaking of space-time symmetries is investigated and extended up to supergravity. Problems of the Higgs gravitation vacuum and its matter sources are discussed. A particular “dislocation” structure of a space-time due to Poincaré translation gauge fields and the corresponding modification of Newton’s gravitational potential are predicted.     

Renormalization of a quantum field theory model in a curved space-time with torsion

A quantum field theory model that contains interacting non-Abelian gauge fields, scalar fields, and spinor fields is considered in a curved space-time with torsion. The cone-loop counterterms are found. It is shown that the multiplicative renormalization condition requires a nonminimal coupling of the matter with the gravitational field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 94–100, August, 1985.     

Gravitational Gauge Theory Developed Based on the Stephenson-Kilmister-Yang Equation

A Yang-Mills formulation of Einstein gravity with spin-affine connection as the dynamical variable of gravitational field is suggested based on the Stephenson-Kilmister-Yang (SKY) equation. A physically interesting property of the present formalism is that the Einstein field equation appears as a first-integral solution to the Yang-Mills type gravitational gauge field equation. The gravitational current density, the law of conservation and the gravitational gauge field strength in vierbein formulation are discussed. The present scheme could provide us with new insight into a possible way to include both Yang-Mills field and gravitational gauge field into one framework of generalized vierbein fields.     

Parity violation in a gravitational theory with torsion: A geometrical interpretation

In a space-time with torsion, the action for the gravitational field can be extended with a parity-violating piece. We show how to obtain such a piece from geometry itself, by suitably modifying the affine connection so as to include a pseudo-tensorial part. A consistent method is thus suggested for incorporating parity-violation in the Lagrangians of all matter fields with spin in a space-time background with torsion.     

Gravitational geons on the brane

In this paper, we examine the possibility of static, spherically symmetric gravitational geons on a 3 dimensional brane embedded in a 4+1 dimensional space-time. We choose a specific g _tt for the brane-world space-time metric. We then calculate g _rr analytically in the weak field limit and numerically for stronger fields. We show that the induced field equations on the brane do admit gravitational geon solutions.     

Gauge fields,space-time geometry and gravity

A general framework for the gauge theory of the affine group and its various subgroups in terms of connections on the bundle of affine frames and its subbundles is given, with emphasis on the correct gauging of groups including space-time translations. For consistency of interpretation, the appropriate objects to be identified with gravitational vierbeins in such theories are not the translational gauge fields themselves, but their pull backs,via appropriate bundle homomorphisms, to the bundle of frames. This automatically solves the problems usually encountered in constructing a gauge theory of the conventional sort for groups containing translations. We give a consistent formulation of the Poincare gauge theory and also of the theory based on translational gauge invariance which, in the absence of matter fields with intrinsic spin, gives a local Lorentz invariant theory equivalent to Einstein gravity.     

Higher corrections in the theory of vacuum polarization by an isotropic gravitational field

A version of the effective Lagrangian method is proposed, which proves to be more effective than the well-known Schwinger-de Witt method for solving self-consistent problems concerning polarization of the matter field vacuum by an isotropic gravitational field. The main result of the paper is computation of polarizationinduced corrections of fourth order in space-time curvature and its derivatives, for scalar and vector massive fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 61–68, October, 1989.The authors thank K. A. Bronnikov, V. N. Lukash, V. N. Mel'nikov, V. N. Ponomarev, A. A. Starobinskii, and V. P. Frolov for many useful discussions of the results of this paper.     

Hydrodynamics in theO 4 gravity

We develop hydrodynamics in a new geometrical gravitational theory, calledO ₄ gravity, which we recently proposed. According to this formulation, matter is not necessarily conserved. The nonconservation of matter might have been considerable in an early era of cosmological evolution.     

Gravimagnetism,causality, and aberration of gravity in the gravitational light-ray deflection experiments

Experimental verification of the existence of gravimagnetic fields generated by currents of matter is important for a complete understanding and formulation of gravitational physics. Although the rotational (intrinsic) gravimagnetic field has been extensively studied and is now being measured by the Gravity Probe B, the extrinsic gravimagnetic field generated by the translational current of matter is less well studied. The present paper uses the post-Newtonian parametrized Einstein and light geodesics equations to show that the extrinsic gravimagnetic field generated by the translational current of matter can be measured by observing the relativistic time delay and/or light deflection caused by the moving mass. We prove that the extrinsic gravimagnetic field is generated by the relativistic effect of the aberration of the gravity force caused by the Lorentz transformation of the metric tensor and the Levi–Civita connection. We show that the Lorentz transformation of the gravity field variables is equivalent to the technique of the retarded Lienard–Wiechert gravitational potentials predicting that a light particle is deflected by gravitational field of a moving body from its retarded position so that both general-relativistic phenomena—the aberration and the retardation of gravity—are tightly connected and observing the aberration of gravity proves that gravity has a causal nature. We explain in this framework the 2002 deflection experiment of a quasar by Jupiter where the aberration of gravity from its orbital motion was measured with accuracy 20%. We describe a theory of VLBI experiment to measure the gravitational deflection of radio waves from a quasar by the Sun, as viewed by a moving observer from the geocentric frame, to improve the measurement accuracy of the aberration of gravity to a few percent.     

Local duality, chiral supersymmetry and fermion-like formulation of non-Abelian pure gauge fields

This work generalizes the fermion-like formulation of the Maxwell theory to the non-Abelian Yang–Mills theory without matter fields. This is a new representation of the Lie algebra valued electric and magnetic fields. The resulting equations of motion are invariant under the chiral transformation. In this formulation, duality is a kind of chirality. We may also define local duality transformations in terms of space-time dependent parameters. There is an N=1 supersymmetry for the Dirac-like operator in this representation. Received: 19 June 2000 / Revised version: 10 October 2000 / Published online: 15 March 2001     

Renormalization of Quantum Field Theory in Curved Space-Time and Renormalization Group Equations

The structure of quantum field theory renormalization in curved space-time is investigated. The equations allowing us to investigate the behaviour of vacuum energy and vertex functions in the limit of small distances in the external gravitational field are established. The behaviour of effective charges corresponding to the parameters of nonminimal coupling of the matter with the gravitational field is studied and the conditions under which asymptotically free theories become asymptotically conformally invariant are found. The examples of asymptotically conformally invariant theories are given. On the basis of a direct solution of renormalization group equations the effective potential in the external gravitational field and the effective action in the gravity with the high derivatives are obtained. The expression for the cosmological constant in terms of R²-gravity Lagrangian parameters is given which does not contradict the observable data. Renormalization and renormalization group equations for the theory in curved space-time with torsion are investigated.     

A geometrical interpretation of parity violation in gravity with torsion

In a space-time with torsion, the action for the gravitational field can be extended with a parity-violating piece. We show how to obtain such a piece from geometry itself, by suitably modifying the affine connection so as to include a pseudo-tensorial part. The merit of such an approach is that it provides one with a consistent method for incorporating parity-violation in the Lagrangians for matter fields with arbitrary spin in a space-time background with torsion.     

Gravitational energy-momentum: The Einstein pseudotensor reexamined

By using a suitable two-point scalar field, a covariant formulation of the Einstein pseudotensor is given. A unique choice of scalar field is made possible by examining the role of linear and angular momentum in their correct geometric context. It is shown that, contrary to many text-book statements, linear momentum is not generated by infinitesimal coordinate transformations on space-time. Use is made of the nonintersecting lifted geodesies on the tangent bundle,T M, to space-time, to define a globally regular three-dimensional Lagrangian submanifold ofT M, relative to an observer at some pointz in space-time. By integrating over this submanifold rather than a necessarily singular spacelike hypersurface, gravitational linear and angular momentum, relative toz, are defined, and shown to have sensible physical properties.This essay received an honorable mention from the Gravity Research Foundation for the year 1979-Ed.     

On the Higgs feature of gravity

The gauge gravitation theory, based on the equivalence principle besides the gauge principle, is formulated in the fibre bundle terms. The correlation between gauge geometry on spinor bundles describing Dirac fermion fields and space-time geometry on a tangent bundle is investigated. We show that field functions of fermion fields in presence of different gravitational fields are always written with respect to different reference frames. Therefore, the conventional quantization procedure is applicable to fermion fields only if gravitational field is fixed. Quantum gravitational fields violate the above mentioned correlation between two geometries.     

Using Hamilton-Jacobi Equation to Study the Neutrino Oscillations in the Stationary Space-Time

We study the mass neutrino oscillation by solving Hamilton-Jacobi equation in the Kerr-Newman-Kasuya space-time, as an important example of the stationary space-time, and give the general expression of the oscillation phase. A special case, the geodesic with L=aE is considered. Then, the proper oscillation length is studied carefully. The effects of the gravitational field, the rotating parameter a, the electric charge and magnetic charge on the oscillation length are given. It is worth noting that a blue shift of the oscillation length rather than a red shift takes place as the neutrino travels out of the gravitational field.     

A new Hamiltonian structure for the dynamics of general relativity

A new compact form of the dynamical equations of relativity is proposed. The new form clarifies the covariance of the equations under coordinate transformations of the space-time. On a deeper level, we obtain new insight into the infinite-dimensional symplectic geometry behind the dynamical equations, the decompositions of gravitational perturbations, and the space of gravitational degrees of freedom. Prospects for these results in studying fields coupled to gravity and the quantization of gravity are outlined.This essay was awarded the second prize for 1976 by the Gravity Research Foundation.     

Kosmologische Lösungen der lorentzinvarianten Gravitationstheorie

In the framework of the Lorentz invariant theory of gravitation a cosmology in the flat space-time is investigated. As in the Newtonian cosmology we start from an infinitely extended system of incoherent matter under the influence of its own gravitational field. The field equations, the equations of motion and the world postulate of homogenity and isotropy for geodetic observes lead then to the Friedman equation. In order to handle the coupled system of equations for the gravitational field and the matter a conveniant approximation method is developed. The calculations are carried out in the second order of this method. The Einstein theory, which is in some respect equivalent to the Lorentz invariant theory of gravitation, serves as a guiding principle for our formal developements. On the other hand the flat space-time cosmology presented here, gives rise to a new interpretation of the Einstein Cosmology.