Faraday transport in a curved space-time

A covariant expression is given for the Faraday transport of electromagnetic radiation in a curved space-time.     

Higher-spin fields in a curved space-time

Algebraic constraints are derived for higher-spin fields in a curved space-time manifold. Comparison is made with previously obtained results. A particular solution of the zero-restmass field equations is given for the plane wave Einstein-Maxwell space-times.     

Asymptotic behavior of the effective potential of composite fields in a curved space-time

The asymptotic behavior of the effective action of composite spinor fields in the Yang-Mills theory, interacting with fermions, in a curved space-time, is computed. It is shown that the requirement that the theory be stable in the limit of large curvatures leads to restrictions on the fermionic multiplet contents. The asymptotic behavior of the effective action of composite bosonic fields in quantized R²-gravity with a scalar field is found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 64–68, May, 1988.In conclusion, I have the pleasure of thanking I. L. Bukhbinder for useful discussions.     

Asymptotic behavior of the effective potential of composite fields in a curved space-time

Renormalization group equations are obtained, which allow studying the asymptotic behavior of the effective potential of composite fields in an external gravitational field. For asymptotically free theories, the behavior of the effective potential is found for large values of composite fields and of the space-time curvature.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 93–98, February, 1988.We thank I. V. Tyutin for discussion during the progress of this work.     

Neutrino helicity flip in a curved space-time

In Minkowskian spaces, the helicity of a massless fermion is a conserved quantity. In principle, this property may not hold when gravitational effects are not neglected. In this context, this work proves that the helicity of a massless neutrino is not conserved in curved spaces. In order to show this fact, the time variation of the helicity in the Heisenberg picture is calculated. Also, we verify that the differential cross-section due to helicity flip of a massless neutrino in a curved space does not vanish as a result of the coupling between the spin and the curvature of space-time.     

Effective potential in curved space and cut-off regularizations

We consider derivation of the effective potential for a scalar field in curved space-time within the physical regularization scheme, using two sorts of covariant cut-off regularizations. The first one is based on the local momentum representation and Riemann normal coordinates and the second is operatorial regularization, based on the Fock-Schwinger-DeWitt proper-time representation. We show, on the example of a self-interacting scalar field, that these two methods produce equal results for divergences, but the first one gives more detailed information about the finite part. Furthermore, we calculate the contribution from a massive fermion loop and discuss renormalization group equations and their interpretation for the multi-mass theories.     

Solitary waves on a curved space-time

A nonlinear partial differential equation is derived which admits plane solitary waves on a conformally flat Riemannian space-time. The metric is determined by the amplitude of these waves. By interpreting these solitary waves as particles we arrive at the following picture: these particles are confined to regions exhibiting singular (very large) amplitudes in an otherwise continuous wavetrain. There is, thus, no distinction between the notion of a particle and that of a wave.     

Conservation theorems in curved space-time

Basic theorems on conservation laws in general space-time are given. The proofs are based on Gauss' theorem which works with ordinary divergence and not with covariant divergence. Consequences for the gravitational theory are exhibited.     

Quantum mechanics in curved space-time

In this paper, the principles of the general relativity are used to formulate quantum wave equations for spin-0 and spin-1/2 particles. More specifically, the equations are worked in a Schwarzschild like metric. As a test, the hydrogen atom spectrum is calculated. A comparison of the calculated spectrum with the numerical data of the deuterium energy levels shows a significant improvement of the accord, and the deviations are almost five times smaller then the ones obtained with the Dirac theory. The implications of the theory considering the strong interactions are also discussed.Received: 27 January 2005, Revised: 15 April 2005, Published online: 31 May 2005     

Hadamard renormalization in curved space-time

We derive the family of all Hadamard symmetric kernels for a quantum massive scalar field propagating at a classical curved background, which can be constructed in terms of purely local geometric quantities. No such kernal exists in the massless limit, unless “restricted geometric objects”, which only have a meaning at conformally flat metrics, are used in its construction. We discuss the relation of this result with the anomalous trace of the renormalized vacuum expectation value of the energy-momentum tensor in the case of conformal triviality. Trace anomaly is shown to be inevitable, if the renormalization recipe is defined in terms of purely geometric quantities, as a consequence of the inexistence of a geometric generalization encompassing every possible space-time of the well-known conformal-vacuum at Robertson-Walker universes.     

弯曲时空中的热平衡

讨论了弯曲时空的一种特殊情况--稳态时空中的热平衡条件,利用普朗克黑体辐射定律和广义相对论,得出了两系统通过辐射而达到热平衡时坐标温度相等,但固有温度不相等的结论.     

Conformal anomalies in curved space-time

The general form of the conformal anomaly in a dimensionally regularized theory of massless fermions in a background metric is shown to be determined by the first few terms of weak field perturbation theory.     

Sine-Gordon equation in curved space-time

We study the static solution of the sine-Gordon wave equation in a background geometry determined by a point mass in 1+1 dimension.     

Dual charged solution in curved space-time

A dual charged solution carrying both electric and magnetic charge is formulated in SU(2) × U(1) gauge theory without making use of the topological characteristics of Higgs fields. When Dirac quantisation condition is imposed, two consequences follow: (i) Weinberg angle is restricted to the value sin² θ = 1/2 and (ii) the solution cannot have fractional electric change, but must have integer items the basic electric charge of the theory. The infinity inherent in the theory is removed at the classical level by the use of gravitational effects by obtaining the same solution in the curved space-time. The resultant metric is of Reissner-Nordström form.