Variational principle and energy-momentum tensor for relativistic electrodynamics of point charges

We give a new representation as tempered distribution for the energy-momentum tensor of a system of charged point-particles, which is free from divergent self-interactions, manifestly Lorentz-invariant and symmetric, and conserved. We present a covariant action for this system, that gives rise to the known Lorentz-Dirac equations for the particles and entails, via Noether theorem, this energy-momentum tensor. Our action is obtained from the standard action for classical electrodynamics, by means of a new Lorentz-invariant regularization procedure, followed by a renormalization. The method introduced here extends naturally to charged p-branes and arbitrary dimensions.     

Group representation theory in relativistic electrodynamics

Invariant expansions of the electromagnetic field tensor F and its covariant derivative ℬF in the presence of gravity are obtained on the basis of the classical problem of elementary orthogonal group representation theory regarding the expansion of the tensor product of representations in terms of irreducible components. Vladimirsk State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 90–93, May, 1996.     

The causality principle in relativistic gravitation theory

It is shown that relativistic gravitation theory is consistent with the existence of vacuum-like medium. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 20–25, April, 2007.     

Symmetries and asymmetries in classical and relativistic electrodynamics

By a comparison between Maxwell's electrodynamics classically interpreted (MT) and relativistic electrodynamics (RED), this paper discusses whether the asymmetries in MT mentioned by A. Einstein in his 1905 relativity paper are only of a conceptual nature or rather involve specific empirical claims. It is shown that in fact MT predicts strongly asymmetric behaviour for very simple interactions, and an analysis is made of the extent of the symmetry achieved by means of relativistic postulates. A low velocity experiment is suggested which could provide another test of the accuracy of RED with respect to MT.     

The variational principle of general relativity

It is shown that the field equations of general relativity never afford a minimum or maximum-not even locally-to the action integralI. Solutions of the field equations always represent a stationary value ofI.     

Radiative damping of a relativistic electron in classical electrodynamics

An exact solution of the problem of the reaction of the field generated by a relativistic classical electron is derived. It is found that the solution differs dramatically from the known formulas by the presence of a component that is even under time reversal. It is also shown that the component of the generalized radiative damping force that is odd under time reversal coincides with the well-known relativistic damping force obtained from the approximate nonrelativistic formula via a Lorentz transformation. Zh. éksp. Teor. Fiz. 114, 1661–1671 (November 1998)     

Variational principle for electrodynamics of moving particles

A consistent relativistic theory of the classical Maxwell field interacting with classical, charged, point-like particles, proposed in [1], is now derived from a variational principle. For this purpose a new electrodynamical Lagrangian based on fluxes is constructed. As a result, we obtain the action principle where i) field degrees of freedom and particle degrees of freedom are kept at the same footing, ii) contrary to the standard formulation, no infinities arise, iii) energy (Hamiltonian) is obtained from the Lagrangian via the Legendre transformation, without any need of adding a complete divergence.     

A variational formulation of relativistic hydrodynamics

We combine Taub's and Ray's variational approaches to relativistic hydrodynamics of perfect fluids into another simple formulation.     

The Schwinger variational principle for the rearrangement collisions

The Lippmann-Schwinger equations were rewritten in the form of Faddeev equations. The number of equations is determined by the number of open channels. On the basis of the Schwinger variational principle the approximate one-dimensional equations for the rearrangement collisions are obtained.Submitted to the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.In conclusion the authors wish to thank V. B. Belyaev for useful discussions and interest in this work.     

Hamilton形式的离散变分原理和第一积分

本文的研究表明：离散Hamilton系统的运动方程的第一积分可以通过研究其相空间离散拉格朗日函数的不变性来确定，提出一个类似连续情况的Hamilton形式的离散诺特定理。     

The treatment of nuclear reactions by Kohn's variational principle

The extension of the Kohn-Hulthen variational principle to the multi-channel reaction problem is discussed. It is shown that this method leads to a unitaryS-matrix. As an application of the method a four channel calculation for the 3/2⁺ state of⁵Li is presented.     

Time-dependent variational principle for quantum lattices

We develop a new algorithm based on the time-dependent variational principle applied to matrix product states to efficiently simulate the real- and imaginary-time dynamics for infinite one-dimensional quantum lattices. This procedure (i) is argued to be optimal, (ii) does not rely on the Trotter decomposition and thus has no Trotter error, (iii) preserves all symmetries and conservation laws, and (iv) has low computational complexity. The algorithm is illustrated by using both an imaginary-time and a real-time example.     

The bogolyubov variational principle in the theory of an anharmonic crystal

The Bogolyubov variational principle for classical systems is used to obtain the variation equation for a self-consistent field. With the help of this equation, various approximations of the self-consistent field method in the theory of a crystal with a multiparticle interaction are studied. The free energy of the crystal is calculated.     

Hamilton formalism and variational principle construction

It is widely accepted that a variational principle cannot be constructed for an arbitrary differential equation; a rigorous mathematical condition shows which equations can have a variational formulation. On the other hand, the importance for variational principles in various fields of physics resulted in several methods to circumvent this condition and to construct another type of variational principles for any differential equation. In this paper the common origin of the considered methods is investigated, and a generalized Hamiltonian formalism is formulated. Additionally, constructive algorithms are given by different methods to construct variational principles. Simple examples are presented to make construction methods more transparent: several Lagrangians are constructed for the different forms of the Maxwell equations and for the extended heat conduction equation.     

A variational principle for symplectic connections

We introduce a variational principle for symplectic connections and study the corresponding field equations. For two-dimensional compact symplectic manifolds we determine all solutions of the field equations. For two-dimensional non-compact simply connected symplectic manifolds we give an essentially exhaustive list of solutions of the field equations. Finally we indicate how to construct from solutions of the field equations on (M, ω) solutions of the field equations on the cotangent bundle to M with its standard symplectic structure.     

A variational principle for Newton-Cartan theory

In the framework of a space-time theory of gravitation a variational principle is set up for the gravitational field equations and the equations of motion of matter. The general framework leads to Newton's equations of motion with an unspecified force term and, for irrotational motion, to a restriction on the propagation of the shear tensor along the streamlines of matter. The field equations obtained from the variation are weaker than the standard field equations of Newton-Cartan theory. An application to fluids with shear and bulk viscosity is given.     

A variational principle for black holes

It is shown that the initial data which gives rise to stationary black hole solutions extremizes the mass for a given angular momentum and area of the horizon. The only extremum of the mass for a given area of the horizon but arbitrary angular momentum is the Schwarzschild solution. In this case, and when the angular momentum is small, the extremum of the mass is a local minimum. This suggests that the initial data for the Schwarzschild solution has a smaller mass than any other initial data with the same area of the horizon. If this is the case, there is no possibility of proving the occurrence of naked singularities by methods suggested by Penrose and Gibbons. Together with Carter's theorem, the fact that the extremum is a local minimum indicates that the Kerr solutions are stable against axisymmetric perturbations.