A natural scalar field in the einstein gravitational theory

In a Riemannian space-time, the difference between the third-order tensor potentialH of the Riemann tensor (presented in a precedent paper) and the Lanczos generating function of the Weyl tensor is here shown to be characterized by a vectorV , obtained by contractionH . The significant role of such a vector, in the context of general relativity, is then discussed. Particular attention is paid to the scalar potential which characterizes the irrotational part ofV : such a scalar field satisfies a space-time wave equation of the Poisson type. Weak fields are also considered: in the particular case of a static metric, the scalar is found to be proportional to the classic Newtonian potential.This work was done in the sphere of activity of the C.N.R. Groups for mathematical research.     

Renormalization in the theory of a quantized scalar field interacting with a robertson-walker spacetime

We demonstrate the possibility of removing the divergences in the energy-momentum tensor by identifying divergent terms with renormalizations of the coupling constants in the gravitational field equation, modified to include a cosmological term and terms quadratic in the curvature. The model studied is that of a classical Robertson-Walker metric and a quantized minimally coupled neutral scalar field. The theory is constructed first with an ultraviolet cutoff as a phenomenological ansatz. The cutoff is then removed in an attempt to obtain a more fundamental theory, whereupon the question arises of the covariance and uniqueness of the resulting renormalized energy-momentum tensor. In the case of a massless field in a spatially flat universe, an apparent infrared divergence is discussed from the point of view of operational determination of the renormalized coupling constants. In the other cases, although the divergences are successfully accounted for by renormalization, we are left with finite leading terms which do not appear to be identifiable with geometrical tensors; the significance of this result is under investigation. If these anomalous terms are dropped, the renormalized energy-momentum tensor agrees with that defined by adiabatic regularization, provided that the limit of slow time variation taken in that method is generalized to a limit of “spacetime flatness.”     

Asymptotic freedom in the theory of a scalar field interacting with quantum R2 gravitation

Conclusions We considered asymptotic freedom in R₂ gravitation interacting with N scalar fields. Numerical analysis of the beta functions showed that asymptotic freedom holds for all N; for N 500, only unstable solutions of the fixed-point equations exist.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 112–116, November, 1991.     

One-loop divergences of linear gravity with torsion terms

We investigate the role of the torsion field at the quantum level. One-loop counterterms are calculated in the theory with terms quadratic in the torsion field. We have shown that the theory is finite at the one-loop level.     

Viscous fluid universe interacting with scalar field

Taking a spherically symmetric isotropic line element, the case of a viscous fluid distribution interacting with scalar field is investigated. Four new solutions are obtained and the models are found to be expanding ones. Their physical and geometrical properties are studied.     

Radiating fluid distribution interacting with scalar field

Taking the combined energy-momentum tensor for a perfect fluid, radially expanding the radiation and zero-mass scalar field, we investigate their interaction and obtain five new analytic solutions in a spherically symmetric Einstein universe. For the corresponding models various physical and geometrical properties are discussed. In one case an interesting equation of state is derived.     

One-loop string corrections to the effective field theory

We calculate the parity-conserving one-loop string corrections to the bosonic part of the 10-dimensional effective field theory for the heterotic string. There is no renormalization of the Chamseddine-Chapline-Manton supergravity action, but terms of fourth order in the curvature tensors are generated. Most of these are of the same forms as those found at the tree level of the string topological expansion, such as (TrR²)², (TrR²)(TrF²) and (TrF²)². However, we also find a non-zero Tr(F⁴) coupling which was not present at the tree level. We comment on the phenomenological implications of these results, which include absences of renormalization of the Kähler metric and of the gauge kinetic function of the effective field theory in four dimensions after compactification, and a modification of the classical equations to be obeyed by the manifold of compactification.     

Absorption and radiation of nonminimally coupled scalar field from charged BTZ black hole

In this paper we investigate the absorption and radiation of nonminimally coupled scalar field from the charged BTZ black hole. We find the analytical expressions for the reflection coefficient, the absorption cross section and the decay rate in strong coupling case. We find that the reflection coefficient is directly governed by Hawking temperature \(T_{H}\), scalar wave frequency \(\omega \), Bekenstein–Hawking entropy \(S_{BH}\), angular momentum m and coupling constant \(\xi \).     

One-loop divergences in chiral perturbation theory and right-invariant metrics onSU(3)

In the framework of chiral perturbation theory, we compute the one-loop divergences of the effective Lagrangian describing strong and non-leptonic weak interactions of pseudoscalar mesons. We use the background field method and the heat-kernel expansion, and underline the geometrical meaning of the different terms, showing how the right-invariance of the metrics onSU(3) allows to clarify and simplify the calculations. Our results are given in terms of a minimal set of independent counterterms, and shorten previous ones of the literature, in the particular case where the electromagnetic fild is the only external source which is considered. We also show that a geometrical construction of the effective Lagrangian at orderO(p ⁴) allows to derive some relations between thefinite parts of the coupling constants. These relations do not depend on the scale used to renormalize.     

Monte carlo simulation of a nucleon interacting with a neutral scalar boson field

A recently proposed Monte Carlo algorithm to solve a Schrödinger equation expressed in Fock-space representation, suitable for the case of hamiltonians describing problems in one-dimensional discrete momentum space, is now extended to the one-, two- and three-dimensional continuous k-spaces. This extension is tested by employing it for an analytically solvable hamiltonian. For this purpose the ‘static source’ limit of the hamiltonian corresponding to the interaction between a nucleon and a neutral, scalar boson field is simulated. The results of the Monte Carlo procedure reproduce very well the exact solution.