Relativistic n-body wave equations in scalar quantum field theory

The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic n-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic n-body wave equations. The equations are shown to have the Schrödinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the n-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields.     

Geodesic Motion of Particles and Quantum Tunneling from Reissner-Nordström Black Holes in Anti-de Sitter Spacetime

The geodesics of tunneling particles were derived unnaturally and awkwardly in previous works. For one thing, the previous derivation was inconsistent with the variational principle of action. Moreover, the definition of geodesic equations for massive particles was quite different from that of massless case. Even worse, the relativistic and nonrelativistic foundations were mixed with each other during the past derivation of geodesics. As a highlight, remedying the urgent shortcomings, we improve treatment to derive the geodesic equations of massive and massless particles in a unified and self-consistent way. Besides, we extend to investigate the Hawking radiation via tunneling from Reissner-Nordström black holes in the context of AdS spacetime. Of special interest, the trick of utilizing the first law of black hole thermodynamics manifestly simplifies the calculation of tunneling integration.     

Universal description of spinning test particles

The unified set of equations of motion for massive or massless spinning test particles is directly established by using a generalized evolution space formalism over the extended space-time including both Newtonian and Einsteinian universes.     

Variational derivation of nuclear hydrodynamics

Equations of nuclear motion are derived from a time-dependent variational principle. They have the same form as the equations of classical hydrodynamics for irrotational flow, and can described motions with arbitrary amplitudes. The theory also gives an equation of state for the nuclear medium.     

Renormalization group and infrared behaviour in theories with coupled massless fields

The renormalization-group method is applied to investigate the infrared singularities in gauge theories with Abelian or non-Abelian symmetry, involving both massive and massless fermions. In the Abelian gauge model the infrared structures of massive and massless fermion propagators and of a massive fermion form factor are found. In the non-Abelian gauge model (quantum chromodynamics) the infrared behaviour of a massless gluon propagator and a massive quark form factor is considered in the logarithmic approximation.     

Effective Action for Scalar Fields in Two-Dimensional Gravity

We consider a general two-dimensional gravity model minimally or nonminimally coupled to a scalar field. The canonical form of the model is elucidated, and a general solution of the equations of motion in the massless case is reviewed. In the presence of a scalar field all geometric fields (zweibein and Lorentz connection) are excluded from the model by solving exactly their Hamiltonian equations of motion. In this way the effective equations of motion and the corresponding effective action for a scalar field are obtained. It is written in a Minkowskian space-time and does not include any geometric variables. The effective action arises as a boundary term and is nontrivial both for open and closed universes. The reason is that unphysical degrees of freedom cannot be compactly supported because they must satisfy the constraint equation. As an example we consider spherically reduced gravity minimally coupled to a massless scalar field. The effective action is used to reproduce the Fisher and Roberts solutions.     

On Approximate Solutions to the Wavefront Speed Problem

We propose an approximate method to obtain the speed of wavefronts. It is built up from a known variational principle. For a range of systems of biological and physical interest, comparison to previously-known solutions and to numerical simulations shows the powerfulness of our approximate technique. For time-delayed equations, we also propose an alternative approximate solution, based on the renormalization group approach, and we compare both approximations.     

A New Variational Principle for the Fundamental Equations of Classical Physics

In this paper we introduce a variational principle from which the fundamental equations of classical physics can be deduced. This principle permits a sort of unification of the gravitational and the electromagnetic fields. The basic point of this variational principle is that the world-line of a material point is parametrized by a parameter a which carries some physical information, namely it is related to the rest mass and to the charge. In particular, the (inertial) rest mass will not be a property of a material point, but it will be a constant of the motion which is determined by the initial conditions. In this framework the equality between the inertial and gravitational mass can be deduced.     

Derivation of an adiabatic time-dependent Hartree-Fock formalism from a variational principle

A derivation of the adiabatic time-dependent Hartree-Fock formalism is given, which is based on a variational principle analogous to Hamilton's principle in classical mechanics. The method leads to a Hamiltonian for collective motion which separates into a potential and a kinetic energy and gives mass and potential parameters in terms of the nucleon-nucleon interaction. The adiabatic approximation assumes slow motion but not small amplitudes and can therefore describe anharmonic effects. The RPA is a limiting case where both amplitudes and velocities are small. The variational approach provides a consistent way of extracting coordinates and momenta from the density matrix and of obtaining equations of motion when particular trial forms for this density matrix are chosen. One such choice leads to Thouless-Valatin formula. An other choice leads to irrotational hydrodynamics.     

Allgemeinrelativistisches Variationsprinzip für Flüssigkeiten und Festkörper in Eulerschen Koordinaten

The basic equations of the general relatiyistic continuum mechanics are derived in Eulerian coordinates by a variational principle with subsidiary conditions. For liquids and solids the Einsteinian field equations with the attached energy-momentum tensor and the adequate equations of motion for the mechanical and thermodynamical quantities follow. The subsidiary conditions are on the one hand physical requirements for system and processes (reversibility, particle conservation), on the other hand consequences of definitions (normalization of velocity). Lin's principle of the identity of particles is discussed. It is necessary as a subsidiary condition.     

Expanding and collapsing scalar field thin shell

This paper deals with the dynamics of scalar field thin shell in the Reissner-Nordstr?m geometry. The Israel junction conditions between Reissner-Nordstr?m spacetimes are derived, which lead to the equation of motion of scalar field shell and Klien–Gordon equation. These equations are solved numerically by taking scalar field model with the quadratic scalar potential. It is found that solution represents the expanding and collapsing scalar field shell. For the better understanding of this problem, we investigate the case of massless scalar field (by taking the scalar field potential zero). Also, we evaluate the scalar field potential when p is an explicit function of R. We conclude that both massless as well as massive scalar field shell can expand to infinity at constant rate or collapse to zero size forming a curvature singularity or bounce under suitable conditions.     

Variational principle for derivation of macroscopic equations

It is pointed out that the Schwinger variational principle of scattering theory applies to the case of linear and nonlinear relaxation problems in quantum statistics. By means of this principle it is possible to derive closed sets of equations for expectation values. To illustrate this variational method and to clarify the connection to other standard approaches some simple examples are treated for which the equations of motion are already known.     

Cherenkov radiation from jets in heavy-ion collisions

The possibility of Cherenkov-like gluon bremsstrahlung in dense matter is studied. We point out that the occurrence of Cherenkov radiation in dense matter is sensitive to the presence of partonic bound states. This is illustrated by a calculation of the dispersion relation of a massless particle in a simple model in which it couples to two different massive resonance states. We further argue that detailed spectroscopy of jet correlations can directly probe the index of refraction of this matter, which in turn will provide information about the mass scale of these partonic bound states.     

CFT adapted gauge invariant formulation of arbitrary spin fields in AdS and modified de Donder gauge

Using Poincaré parametrization of AdS space, we study totally symmetric arbitrary spin massless fields in AdS space of dimension greater than or equal to four. CFT adapted gauge invariant formulation for such fields is developed. Gauge symmetries are realized similarly to the ones of Stueckelberg formulation of massive fields. We demonstrate that the curvature and radial coordinate contributions to the gauge transformation and Lagrangian of the AdS fields can be expressed in terms of ladder operators. Realization of the global AdS symmetries in the conformal algebra basis is obtained. Modified de Donder gauge leading to simple gauge fixed Lagrangian is found. The modified de Donder gauge leads to decoupled equations of motion which can easily be solved in terms of the Bessel function. Interrelations between our approach to the massless AdS fields and the Stueckelberg approach to massive fields in flat space are discussed.     

Lagrange method and boundary conditions for the intensity correlation functions in turbulent media*

Abstract

An exact functional integral representation for the two-point intensity correlation function was previously obtained by the author for a collimated beam wave by solving the moment equation. The variable functions of integration involved therein can be effectively limited to a set of functions determined so that the entire phase term of the integrand becomes stationary against arbitrary variation of the variable functions, exactly according to the Lagrange variational principle in dynamics. The result is free from any expansion and is presented with a set of unperturbed equations of closed form. When making a formal expansion, it leads to the zeroth- and first-order expressions similar to those obtained by an improved two-scale method. With exactly the same procedure, the three-point intensity correlation and the two-frequency intensity correlation were also obtained.The Lagrange method leads to the ‘equation of motion’ subjected to boundary conditions to continue the phase term from the incident beam wave. The boundary conditions were previously found based on a physical reasoning, while the same conditions are found here purely based an the variational principle. A focused beam wave is assumed for the incident wave, including both spherical and plane waves as special cases.     

On\overline {GL(4,\mathbb{R})}-covariant extensions of the Dirac equation

Infinite component generalizations of both massless and massive Dirac equations are constructed which are covariant with respect to the double covering of the general linear group in four dimensions. These generalized Dirac equations can be made covariant with respect to the full diffeomorphism group of the spacetime manifold by replacing ordinary derivatives by covariant derivatives in the usual way.     

On the theory of small-amplitude vibrations of curved-surface diaphragms

An equation is derived describing small-amplitude vibrations of an arbitrary curved diaphragm, whose surface is considered as a two-dimensional Riemannian space. The derivation is based on the variational principle, from which the motion equation and conservation law follow in a form invariant with respect to arbitrary transformations of coordinates on the diaphragm surface. It has been shown that the wave equation, along with the two-dimensional Laplace-Beltrami operator, includes an additional term proportional to the scalar curvature of the diaphragm surface. As an example, the equations are considered for a spherical diaphragm and a catenoid-shaped diaphragm with a minimal surface of revolution.