Manifestations of group covariance in a metric theory

Foundations of Physics - The requirement to present Dirac's Large Number Hypothesis in one system of units in which the resulting modifications to Einstein's theory are exhibited, led to...     

General relativistic theory of gravitation exhibiting complete group covariance

The geometry of the group manifold is generalized to allow the construction of a general relativistic theory exhibiting all the degrees of freedom of the group in its dynamical variables. The theory has features of a multidimensional Kaluza-Klein theory with noncommuting Killing vectors. The resulting fields suggest, however, a teleparallelistic formulation. The geometry and gauge invariance of the theory are discussed.     

Improved routing strategy based on gravitational field theory

Routing and path selection are crucial for many communication and logistic applications. We study the interaction between nodes and packets and establish a simple model for describing the attraction of the node to the packet in transmission process by using the gravitational field theory, considering the real and potential congestion of the nodes. On the basis of this model, we propose a gravitational field routing strategy that considers the attractions of all of the nodes on the travel path to the packet. In order to illustrate the efficiency of proposed routing algorithm, we introduce the order parameter to measure the throughput of the network by the critical value of phase transition from a free flow phase to a congested phase,and study the distribution of betweenness centrality and traffic jam. Simulations show that, compared with the shortest path routing strategy, the gravitational field routing strategy considerably enhances the throughput of the network and balances the traffic load, and nearly all of the nodes are used efficiently.     

Analysis of network traffic flow dynamics based on gravitational field theory

For further research on the gravity mechanism of the routing protocol in complex networks,we introduce the concept of routing awareness depth,which is represented by ρ.On this basis,we define the calculation formula of the gravity of the transmission route for the packet,and propose a routing strategy based on the gravitational field of the node and the routing awareness depth.In order to characterize the efficiency of the method,we introduce an order parameter,η,to measure the throughput of the network by the critical value of phase transition from free flow to congestion,and use the node betweenness centrality,B,to test the transmission efficiency of the network and congestion distribution.We simulate the network transmission performance under different values of the routing awareness depth,ρ.Simulation results show that if the value of the routing awareness depth ρ is too small,then the gravity of the route is composed of the attraction of very few nodes on the route,which cannot improve the capacity of the network effectively.If the value of the routing awareness depth ρ is greater than the network's average distance l,then the capacity of the network may be improved greatly and no longer change with the sustainable increment of routing awareness depth ρ,and the routing strategy performance enters into a constant state.Moreover,whatever the value of the routing awareness depth ρ,our algorithm always effectively balances the distribution of the betweenness centrality and realizes equal distribution of the network load.     

Singularities in gravitational theory

It is shown that in the absolute parallelism theory a unique choice of field equations can be made by requiring that the solutions extend beyond possible singularities, while for the equations of the general theory of relativity and R²-gravitation this condition is not satisfied. The system of equations thus produced is also distinguished by the fact that it makes possible validity of the equivalence principle with certain limitations related to the presence of symmetry.Kemerov State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 73–78, July, 1992.     

Newtonian gravitational field theory

A field theory for gravitation is developed within the framework of the special theory of relativity. This is achieved by exploiting the similarity in mathematical structure of two relations which are found in both Newton's gravitational theory and Maxwell's electromagnetic theory. These relations are: (1) the law of force between the relevant physical entities (mass and electric charge), and (2) the equation of continuity (conservation of charge). The field equations describe the propagation of gravitational waves with the velocity of light in much the same way that Maxwell's field equations describe electromagnetic waves. Both fields have such similar mathematical structures that they are developed in parallel up to the point where their inherently different physical content cause their paths of evolution to diverge. At this stage, the field equations for both theories are determined. The physical significance of the field variables of both theories imposes a mathematical formalism which doesnot give rise to self-interactions. A calculation for the energy in the field of two particles representative of either the electromagnetic or gravitational field is shown to give the correct finite value. The reason that conventional calculations yield an infinite energy is readily seen to lie in the calculation of a physically meaningless quantity. The mathematical formalism required by the field theories is used to develop generalizations of the usual conservation laws. Two conservation laws are derived which are consequences of the consistent physical interpretation of the field variables. These laws do not appear in conventional theory. The approach followed here in developing the field theories leads to the appearance of forces dual to the well-known forces. Thus, for the electromagnetic field, we find a dual to the Lorentz force and, in the gravitational field, we find a dual to Newton's law of gravitation. These results are not due to the introduction of the fields, for they can be expressed in terms of the particle variables. They emerge from the consistent application of the physical interpretation of the particle and field variables. A basic physical principle, which underlies both theories, is best expressed by the statement: It is the interactions between the elements of a physical event and not the elements themselves which are the physical observables.     

Special relativistic gravitational theory

Based on special relativity, we introduce a way to develop a new field theory from (1) the relativistic property of the particle coupling coefficient with the field, and (2) the field due to a static point source. As an example, we discuss a theory of electromagnetic and gravitational fields. The results of this special relativistic gravitational theory for the redshift and the deflection of light are the same as those deduced from general relativity. The results of experiments on the planetary perihelion procession shift and on an additional short-range gravity are more favorable to the special relativistic gravitational theory than to general relativity. We put forward a new idea to test experimentally whether the equivalence principle of general relativity is correct.Plovdiv University Paissii Hilendarskii.Moscow Institute of Railway Transport Engineers.     

Some remarks on general covariance of quantum theory

If one accepts Einstein's general principle of relativity (covariance principle) also for the sphere of microphysics (quantum mechanics, quantum field theory, theory of elementary particles), one has to ask how far the fundamental laws of traditional quantum physics fulfil this principle. The reason for presenting this short paper is to draw attention to a series of papers that have appeared during the last years, in which the author criticized the usual scheme of quantum theory (Heisenberg picture, Schrödinger picture, etc.) and presented a new foundation of the basic laws of quantum physics, obeying the principle of fundamental covariance (Einstein's covariance principle in space-time and covariance principle in Hilbert space of quantum operators and states) [1].Dedicated to Achille Papapetrou on the occasion of his retirement.     

Renormalization group method based on the ionization energy theory

Proofs are developed to explicitly show that the ionization energy theory is a renormalized theory, which mathematically exactly satisfies the renormalization group formalisms developed by Gell–Mann–Low, Shankar and Zinn-Justin. However, the cutoff parameter for the ionization energy theory relies on the energy-level spacing, instead of lattice point spacing in k-space. Subsequently, we apply the earlier proofs to prove that the mathematical structure of the ionization-energy dressed electron–electron screened Coulomb potential is exactly the same as the ionization-energy dressed electron–phonon interaction potential. The latter proof is proven by means of the second-order time-independent perturbation theory with the heavier effective mass condition, as required by the electron–electron screened Coulomb potential. The outcome of this proof is that we can derive the heat capacity and the Debye frequency as a function of ionization energy, which can be applied in strongly correlated matter and nanostructures.     

Conformally invariant gravitational waves in a modified gravitational theory

International Journal of Theoretical Physics - An attempt is made to obtain a conformally invariant gravitational wave equation in an isotropic background universe by modifying the Einstein field...     

A new geometrical gravitational theory

A geometrical gravitational theory based on the connection ={ } + ln + ln –g ln is developed. The field equations for the new theory are uniquely determined apart from one unknown dimensionless parameter ₂. The geometry on which our theory is based is an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metricg and two gauge scalars and. Physically the gravitational potential corresponds tog in the same way as in general relativity, the gravitational coupling constant to ^–2, and the gravitational mass tou(, ), which is a coscalar of power –1 algebraically made of and. The theory satisfies the weak equivalence principle, but breaks the strong one generally. We shall find outu(, )= on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus we have the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power –4 algebraically made of andu(, ), so it is dynamical, too. Finally we give spherically symmetric exact solutions. The permissible range of the unknown parameter ₂ is experimentally determined by applying the solutions to the solar system.     

Scalar-tensor theory of gravitation: Generalizations and experimental limitations

Several theories with scalar field can be derived from different variational principles. Here we consider a very general variational principle and we prove that, in the exterior case without electromagnetic field, the solution for a particular case generates the set of solutions for the general case. This is applied to the exterior solution in the static case with spherical symmetry without electromagnetic field. We investigate the predictions for the classic effects and the event horizons. Then we get some limitations for the variational principles which generalize the usual limitations. In all these cases the Schwarzschild solution with his horizon appears as a very particular case.     

Hamiltonian structure of gravitational field theory

Hamiltonian generalizations of Einstein's theory of gravitation introducing a laminar structure of spacetime are discussed. The concepts of general relativity and of quasi-inertial coordinate systems are extended beyond their traditional scope. Not only the metric, but also the coordinate system, if quantized, undergoes quantum fluctuations.     

Two dimensional lattice gauge theory based on a quantum group

In this article we analyse a two dimensional lattice gauge theory based on a quantum group. The algebra generated by gauge fields is the lattice algebra introduced recently by A.Yu. Alekseev, H. Grosse and V. Schomerus in [1]. We define and study Wilson loops. This theory is quasi-topological as in the classical case, which allows us to compute the correlation functions of this theory on an arbitrary surface.Laboratoire Propre du CNRS UPR 14     

A new unified field theory based on the conformal group

We develop here a new unified theory of the electromagnetic and gravitational field, based on a six-dimensional generalization of Maxwell's equations; additional space-time coordinates are interpreted only as mathematical tools in order to obtain a linear realization of the four-dimensional conformal group.     

General covariance violation and the gravitational dark matter: Vector graviton

The (four-component) vector graviton contained in the metric, the scalar component incorporated, is attributed to the violation of the general covariance to the residual isoharmonic one. In addition to the previously studied (singlet) scalar graviton, the vector graviton may constitute one more fraction of the gravitational dark matter. The gravity interactions of the vector graviton, as well as its impact on the continuous medium, are studied. The text was submitted by the author in English.     

General covariance violation and the gravitational dark matter: Scalar graviton

The violation of the general covariance is proposed as a resource of the gravitational dark matter. The minimal violation of the covariance to the unimodular one is associated with the massive scalar graviton as the simplest representative of such matter. The Lagrangian formalism for a continuous medium, a perfect fluid in particular, in the scalar graviton environment is developed. The implications for cosmology are briefly indicated. The text was submitted by the author in English.     

A mathematical theory of gravitational collapse

We study the asymptotic behaviour, as the retarded timeu tends to infinity, of the solutions of Einstein's equations in the spherically symmetric case with a massless scalar field as the material model. We prove that when the final Bondi massM ₁ is different from zero, asu , a black hole forms of massM ₁ surrounded by vacuum. We find the rate of decay of the metric functions and the behaviour of the scalar field on the horizon.Research supported in part by National Science Foundation grants MCS-8201599 to the Courant Institute and PHY-8318350 to Syracuse University