Asymptotic safety in Einstein gravity and scalar-fermion matter

Within the functional renormalization group approach we study the effective quantum field theory of Einstein gravity and one self-interacting scalar coupled to N(f) Dirac fermions. We include in our analysis the matter anomalous dimensions induced by all the interactions and analyze the highly nonlinear beta functions determining the renormalization flow. We find the existence of a nontrivial fixed point structure both for the gravity and the matter sector, besides the usual Gaussian matter one. This suggests that asymptotic safety could be realized in the gravitational sector and in the standard model. Nontriviality in the Higgs sector might involve gravitational interactions.     

On the unification of electroweak interactions with gravity

It is shown that the electroweak interactions in the Salam-Weinberg model can be described by a space-time connection form which preserves the space-time metric multiplied by a conformal factor. In addition, one needs an extraSO(2)-connection form. The Dirac field in this formalism is described (after making a certain regularity assumption) by a vierbein field for the space-time metric and a complex scalar field.Invited talk at the Intarnational Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–21, 1981.     

Strong gravity and weak interactions

The strong gravity contribution to the nucleonic axial-vector form factor is evaluated in the nonrelativistic limit and in the approximation of exactSU ₃ symmetry. It is suggested also that the anomalous experimental results on the value of the axial coupling constant, in very light nuclei, may be explained as being an effect due to strong gravitational interactions.     

Inflation in Einstein-Cartan theory with energy-momentum tensor with spin

Generalized, or “power-law”, inflation is shown to necessarily exist for a simple, anisotropic, (Bianchi type I) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley improved energy-momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density.     

Induced gravity and gauge interactions revisited

It has been shown that the primary, old-fashioned idea of Sakharov's induced gravity and gauge interactions, in the “one-loop dominance” version, works astonishingly well yielding phenomenologically reasonable results. As a byproduct, the issue of the role of the UV cutoff in the context of the induced gravity has been reexamined (an idea of self-cutoff induced gravity). As an additional check, the black hole entropy has been used in the place of the action. Finally, it has been explicitly shown that the induced coupling constants of gauge interactions of the standard model assume qualitatively realistic values.     

Configurations with a vector field in the Einstein-Cartan theory

The properties of self-gravitating distributions of an ideal fluid charged by a vector field which is either massive or massless, i.e., electromagnetic, are considered taking account of the spin properties of the vector field in the framework of the Einstein-Cartan theory of gravitation. Conditions for equilibrium are found and the corresponding exact solutions are obtained. A complete system of first integrals of the corresponding equations of motion is found for dynamical distributions in the absence of pressure. A theorem on the correspondence between the dynamics of an electrically charged ideal fluid with a limiting equation of state and the dynamics of a free massive vector field is also proved.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 7–11, August, 1979.     

The canonical variables,the symplectic structure and the initial value formulation of the generalized Einstein-Cartan theory of gravity

Canonical variables for the generalized (non-metric) Einstein-Cartan theory of gravity are defined. The space of solutions is equipped with a closed differential 2-form . The symplectic 2-form has a diagonal representation in terms of canonical variables. A geometric interpretation of the canonical variables is presented and the 3+1 formulation of the field equations is given.     

Neutrino fields in Einstein-Cartan theory

The spin-coefficient formalism presented elsewhere is here applied to classical neutrino fields in Einstein-Cartan theory. It is shown that the neutrino current vector is tangent to an expansion-free null geodesic congruence with constant and equal twist and shear, which vanish if and only if the congruence is a repeated principal null congruence of the gravitational field. The geodesics are both extremals and autoparallels. All exact solutions for the case of pure radiation fields are obtained, and it is shown that the only possible ghost solutions have a plane wave metric.     

Ghost neutrinos in Einstein-Cartan theory

It is shown that ghost neutrino fields can occur in Einstein-Cartan theory as well as in general relativity, contrary to an earlier result of Letelier.     

First-order invariant Einstein-Cartan variational structures

A first-order invariant Einstein-Cartan structure is a Lagrangian structure on a differential manifold defined by a generally invariant Lagrangian depending on a metric field, a connection field, and the first derivatives of these fields. Moreover, it is assumed that the metric and connection fields satisfy the so-called compatibility condition. In this paper the problem of finding all such invariant Einstein-Cartan structures is discussed. It is shown that each Lagrangian of these structures depends only on certain tensors constructed from the metric and the connection fields, which means that all the Lagrangians can be described within the framework of the classical theory of invariants. The maximal number of functionally independent Lagrangians is determined as a function of the dimension of the underlying manifold.     

A nonstationary cosmological model with rotation in the Einstein-Cartan theory

Within the Einstein—Cartan theory framework, a nonstationary causal cosmological model with a Gödel type metric is constructed for the case when the sources are: the Weissenhoff anisotropic fluid, pure radiation, and heat flux. The model is characterized by expansion, rotation, shift, and acceleration.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 90–94, August, 1993.     

Inflation in the Einstein-Cartan cosmological model

All the three primordial phases of the universe, required by inflation, plus what is believed to be the present phase, have been studied in the Einstein-Cartan cosmological model in a Bianchi type I metric.     

Stochastic Quantization of Einstein-Cartan Gravitational Theory

We apply the stochastic quantization method to Einstein-Cartan gravitational theory. The stochastic propagators are calculated and the cooperation of modes in such a theory is investigated. It was shown that in equilibrium limit our result is equivalent to the propagator for the symmetric part of tetrads.     

Static dust sphere in Einstein-Cartan theory

Physically meaningful solutions of the field equations for static spherical dust distributions in the Einstein-Cartan theory have been obtained. There is one in which the spin is zero at the center and another with zero spin at the boundary of the sphere.     

Asymptotic freedom in the Einstein-Cartan theory

The Einstein-Cartan theory with a cosmological constant and an external current is analyzed. Single-loop contraterms repeat the structure of the original action on the mass shell. This fact is utilized to write a renormalization-group equation for the effective charges associated with the cosmological constant and the square of the current. Asymptotic freedom is realized in the ultraviolet region for the new charges.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 40–44, September, 1988.