On the convergence of planar diagram expansions

Renormalizable quantum field theories whose perturbation expansions are described by planar Feynman diagrams only, such as SU() gauge theory, are considered in 4 dimensional Euclidean space. For studying asymptotic properties of the perturbation series one might wish to isolate first all those planar diagrams that do not contain any ultraviolet divergent subgraphs. In this paper it is proved that this infinite set of diagrams, when summed, converges within a finite radius of convergence for the coupling constant.     

The accuracy of the approximations in classical nucleation theory

The mathematical approximations involved in the theory of homogeneous nucleation are shown to produce negligible error in the predicted rates of nucleation.     

The classical limit of temperature Green's function expansions

Rules are obtained for calculating the classical limit of Green's function diagrammatic expansions. The classical cluster expansion is derived by calculating the classical limit of the exact Green's function. Other operators of interest in linear response theory may be calculated in the classical limit. The retarded real-time spin density correlation function, proportional to the magnetic susceptibility, is shown to be exactly proportional to the density in this limit. The relation of this work to other approaches is discussed.     

The three-particle collision term in quantum kinetic theory

We outline a formalism for obtaining the three-particle collision term in quantum kinetic theory. The scheme is based on expansions in terms of initial distribution functions and Bogoliubov's initial condition of vanishing correlations in the infinite past.     

The post-post-Newtonian problem in classical electromagnetic theory

We find the Lagrangian to order c^?4 for two charged bodies (with $\text{e}{}_1\text{m}{}_1\text{=}\text{e}{}_2\text{m}{}_2$) in electromagnetic theory. This Lagrangian contains acceleration terms in its final form and we show why it is incorrect to eliminate these terms by using the equationsof motion in the Lagrangian as was done by Golubenkov and Smorodinskii, and by Landau and Lifshitz. We find the center of inertia and show that the potential energy term does not split equally between particles 1 and 2 as it does in the Darwin Lagrangian (Lagrangian to order c^?2). In addition to the infinite self-energy terms in the electromagnetic energy-momentum tensor, which are eliminated using Gupta's method, some new type of divergent terms are found in the moment of electromagnetic field energy and in the electromagnetic field momentum which cancel in the final conservation law for the center of inertia.     

Asymptotic expansions in nonlinear regression theory

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 20–25, September, 1995.     

The dirac-schwinger covariance condition in classical field theory

A straightforward derivation of the Dirac-Schwinger covariance condition is given within the framework of classical field theory. The crucial role of the energy continuity equation in the derivation is pointed out. The origin of higher order derivatives of delta function is traced to the presence of higher order derivatives of canonical coordinates and momenta in the energy density functional.     

High-temperature expansions in statistical theory of atomic ordering

In the present article a high-temperature series for the statistical sum of a binary alloy is considered. The study is carried out within a statistical ensemble, corresponding to fixing atomic concentration in certain chosen groups of lattice sites. Diagrammatic technique for calculating the statistical sum of the ensemble indicated is introduced.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 104–108, February, 1982.     

Some problems in the classical theory of radiation

The article considers the problem of the complete radiation of the energy of a charged particle moving in constant and homogeneous electric and magnetic fields and in the field of a plane wave. Exact formulas are obtained for these cases. The problem is al so considered of the instantaneous radiation of an arbitrary moving charge. The problems are considered according to classical theory.     

The classical solutions of the dimensionally reduced gravitational Chern-Simons theory

The Kaluza-Klein reduction of the 3d gravitational Chern-Simons term to a 2d theory is equivalent to a Poisson-sigma model with 4d target space and degenerate Poisson tensor of rank 2. Thus two constants of motion (Casimir functions) exist, namely charge and energy. The application of well-known methods developed in the framework of first order gravity allows to construct all classical solutions straightforwardly and to discuss their global structure. For a certain fine tuning of the values of the constants of motion the solutions of hep-th/0305117 are reproduced. Possible generalizations are pointed out.     

A two-particle collision in aesthetic field theory

We have found a new computer solution to the aesthetic field equations. This solution describes a two-particle system with more structure than previously found. The contour lines show an arm structure. We have observed four arms around the maximum center. The location of the maximum (minimum) center is not along a straight line as a function of time. This is the first time that such an effect has been observed for any kind of nonlinear partial differential equation, so far as we know. A further discussion of the aesthetic principles leading to the field equations is given.     

Centrality of the collision and random matrix theory

I discuss the results from a study of the central 12CC collisions at 4.2 A GeV/c.The data have been analyzed using a new method based on the Random Matrix Theory.The simulation data coming from the Ultra Relativistic Quantum Molecular Dynamics code were used in the analyses.I found that the behavior of the nearest neighbor spacing distribution for the protons,neutrons and neutral pions depends critically on the multiplicity of secondary particles for simulated data.I conclude that the obtained results offer the possibility of fixing the centrality using the critical values of the multiplicity.     

Symmetric linear collision operators in kinetic theory

We consider a class of equilibrium time correlation functions, in fluids, between local physical quantities. We investigate whether the symmetry these correlation functions display with respect to these quantities on theN-particle level also exists on the one-particle (kinetic) level. In this context we derive a new symmetric kinetic operator for a dense, hard sphere fluid.     

Cumulants in perturbation expansions for non-equilibrium field theory

The formulation of perturbation expansions for a quantum field theory of strongly interacting systems in a general non-equilibrium state is discussed. Non-vanishing initial correlations are included in the formulation of the perturbation expansion in terms of cumulants. The cumulants are shown to be the suitable candidate for summing up the perturbation expansion. Also a linked-cluster theorem for the perturbation series with cumulants is presented. Finally, a generating functional of the perturbation series with initial correlations is studied. We apply the methods to a simple model of a fermion-boson system.