A linear relativistic model of processes with causal faster-than-light effects

To get a synthesis of causal faster-than-light effects and signals that do not propagate faster than light by using local, covariant, linear equations of motion, we propose the following hypothesis. Free fields that propagate signals according to the Klein-Gordon, Dirac, Proca or Maxwell equations, are actually describing only smoothed-out, average properties of underlying causal transport processes of point like entities with arbitrary four-momenta, the states of which are described by a scalar, spinor or four-vector field that satisfies a local, covariant, linear transport equation. An example of such a linear, causal, covariant transport process is shown to display causal faster-than-light effects, to propagate signals not faster than light, and to contain the Klein-Gordon equation as a limiting case. An analogous transport model displays causal, four-vector, faster-than-light effects, and also distinctive four-vector, long-range and short-range effects that do not propagate faster than light.     

The quantum relativistic two-body problem in time-dependent external potentials

A two-body system with scalar constituents of finite masses is described by a pair of coupled Klein-Gordon equations. The modification required for preserving compatibility in the presence of an external field is nontrivial but can be exactly carried out beyond the static case when the external potential admits a suitable invariance. The conditions ensuring this property are exhibited assuming that the external field is either electromagnetic or a pure spin-two tensor (like a weak gravitational field). Special attention is devoted to plane waves. A suitable superposition of linearly polarized waves permits to apply this method when the field is electromagnetic. Another example is given by an external spin-two field obeying the propagation equation with a mass term.     

Relativistic wave mechanics of spinless particles in a curved space-time

Starting from the Klein-Gordon equation, the single-particle approximation for a reiativistic scalar particle in the presence of external electromagnetic and gravitational fields is performed. The nonrelativistic limit is obtained by a Foldy-Wouthuysen transformation on a Schrödinger-type equation. The results are then compared with those obtained in classical mechanics.     

Indefinite charge for the classical spinor field

We define a conserved Lorentz vector for a two-component spinor field that obeys the Klein-Gordon equation and interpret it as a charge-current density. The corresponding total charge can take negative as well as positive values, which is not the case for the usual charge of the Dirac field. We consequently can define probability amplitudes for a relativistic quantum mechanics, and we solve the inhomogeneous equation by means of the causal Green function. This vector is not invariant under gauge transformations of the spinor field, and we cannot generalize the equation by the gauge invariant substitution to obtain the interaction with an electromagnetic field. In the limit of a massless field that obeys the Weyl equation, the charge vanishes.     

A Generally Covariant Wave Equation for Grand Unified Field Theory

A generally covariant wave equation is derived geometrically for grand unified field theory. The equation states most generally that the covariant d'Alembertian acting on the vielbein vanishes for the four fields which are thought to exist in nature: gravitation, electromagnetism, weak field and strong field. The various known field equations are derived from the wave equation when the vielbein is the eigenfunction. When the wave equation is applied to gravitation the wave equation is the eigenequation of wave mechanics corresponding to Einstein's field equation in classical mechanics, the vielbein eigenfunction playing the role of the quantized gravitational field. The three Newton laws, Newton's law of universal gravitation, and the Poisson equation are recovered in the classical and nonrelativistic, weak-field limits of the quantized gravitational field. The single particle wave-equation and Klein-Gordon equations are recovered in the relativistic, weak-field limit of the wave equation when scalar components are considered of the vielbein eigenfunction of the quantized gravitational field. The Schrödinger equation is recovered in the non-relativistec, weak-field limit of the Klein-Gordon equation). The Dirac equation is recovered in this weak-field limit of the quantized gravitational field (the nonrelativistic limit of the relativistic, quantezed gravitational field when the vielbein plays the role of the spinor. The wave and field equations of O(3) electrodynamics are recovered when the vielbein becomes the relativistic dreibein (triad) eigenfunction whose three orthonormal space indices become identified with the three complex circular indices (1), (2), (3), and whose four spacetime indices are the indices of non-Euclidean spacetime (the base manifold). This dreibein is the potential dreibein of the O(3) electromagnetic field (an electromagnetic potential four-vector for each index (1), (2), (3)). The wave equation of the parity violating weak field is recovered when the orthonormal space indices of the relativistic dreibein eigenfunction are identified with the indices of the three massive weak field bosons. The wave equation of the strong field is recovered when the orthonormal space indices of the relativistic vielbein eigenfunction become the eight indices defined by the group generators of the SU (3) group.     

Causal interpretation of the modified Klein-Gordon equation

A consistent causal interpretation of the Klein-Gordon equation treated as a field equation has been developed, and leads to a model of entities described by the Klein-Gordon equation, i.e., spinless, massive bosons, as objectively existing fields. The question arises, however, as to whether a causal interpretation based on a particle ontology of the Klein-Gordon equation is also possible. Our purpose in this article will be to indicate, by making what we believe is a best possible attempt at developing a particle interpretation of the Klein-Gordon equation, that such an interpretation is untenable. To resolve the nonpositive-definite probability density difficulties with the Klein-Gordon equation, we modify this equation by the introduction of an evolution parameter. We base our subsequent considerations on this modified Klein-Gordon equation. Partly to motivate the need for a relativistic causal interpretation and partly to give emphasis to aspects of the causal interpretation often overlooked, we begin our article with a brief historical survey of the causal interpretation.Other work commitments prevented publication of this article in the special issue ofFoundations of Physics in honor of Prof. J. P. Vigier. I would nevertheless like to dedicate this work to Prof. Vigier in recognition of this untiring contributions to the causal interpretation in particular and to the foundations of physics in general. I take this opportunity to thank Prof. Vigier for his help during my Royal Society fellowship spent at the Institut Henri Poincaré in the academic year 1988–1989.     

Investigation of Green's functions in an external electromagnetic field by the eigenfunction method

This paper contains a study of Green's functions in a quantum electrodynamics (QED) with an external electromagnetic field that disrupts vacuum stability. Representations are found for the Green's functions of a scalar QED in the eigenfunction basis of Klein-Gordon equations for a uniform constant electromagnetic field in combination with the field of a plane wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 70–74, June, 1989.     

引力场中标量粒子波方程的玻姆量子势描述

对于引力场中标量粒子的Klein-Gordon方程,在引入玻姆量子势后,可写出类似于经典粒子的轨道运动方程,继而可表示成重新定义的度规空间中的测地线方程。     

U(1) gauge theory of the quantum hall effect

The solution of the Klein-Gordon equation for a complex scalar field in the presence of an electrostatic field orthogonal to a magnetostatic field is analyzed. Considerations concerning the quantum Hall-type evolution are presented also. Using the Hamiltonian with a self-interaction term, we obtain a critical value for the magnetic field in the case of the spontaneous symmetry breaking.     

Klein-Gordon方程Q球解中能量稳定性和扰动研究

本文研究了一种复标量场模型中的双层Q球解,在解析形式下计算了Q球荷和能量. 同时,分析了其能量稳定性质,通过Klein-Gordon 方程获得了Q球能量的扰动表达式. 另外,还讨论了Q球暗物质产生的物理效应. 关键词： Klein-Gordon方程 Q球解 能量稳定性与扰动 暗物质     

On Some Solutions of Relativistic Wave Equations

In this paper we present exact solutions of the Klein-Gordon and the Dirac equations in different configurations of an electromagnetic field, which are characteristic for free-electron laser-type gauges. In the case of motion of a charge scalar particle in standing wave an energy spectrum is studied. For the motion of an electron in a so-called wiggler magnetic field a spinor wave function is proved to be obtainable. An undulator field configuration with propagating wave is treated also.     

Identical motion in relativistic quantum and classical mechanics

The Klein-Gordon equation for the stationary state of a charged particle in a spherically symmetric scalar field is partitioned into a continuity equation and an equation similar to the Hamilton-Jacobi equation. There exists a class of potentials for which the Hamilton-Jacobi equation is exactly obtained and examples of these potentials are given. The partitionAnsatz is then applied to the Dirac equation, where an exact partition into a continuity equation and a Hamilton-Jacobi equation is obtained.     

Exact Klein-Gordon equation with spatially dependent masses for unequal scalar-vector Coulomb-like potentials

We study the effect of spatially dependent mass functions over the solution of the Klein-Gordon equation in the (3 + 1 -dimensions for spinless bosonic particles where the mixed scalar-vector Coulomb-like field potentials and masses are directly proportional and inversely proportional to the distance from the force center. The exact bound-state energy eigenvalues and the corresponding wave functions of the Klein-Gordon equation for mixed scalar-vector and pure scalar Coulomb-like field potentials are obtained by means of the Nikiforov-Uvarov (NU) method. The energy spectrum is discussed for different scalar-vector potential mixing cases and also for the constant-mass case.     

Quantum mechanics of Klein-Gordon fields I: Hilbert Space, localized states, and chiral symmetry

We derive an explicit manifestly covariant expression for the most general positive-definite and Lorentz-invariant inner product on the space of solutions of the Klein-Gordon equation. This expression involves a one-parameter family of conserved current densities , with a ∈ (−1, 1), that are analogous to the chiral current density for spin half fields. The conservation of is related to a global gauge symmetry of the Klein-Gordon fields whose gauge group is U (1) for rational a and the multiplicative group of positive real numbers for irrational a. We show that the associated gauge symmetry is responsible for the conservation of the total probability of the localization of the field in space. This provides a simple resolution of the paradoxical situation resulting from the fact that the probability current density for free scalar fields is neither covariant nor conserved. Furthermore, we discuss the implications of our approach for free real scalar fields offering a direct proof of the uniqueness of the relativistically invariant positive-definite inner product on the space of real Klein-Gordon fields. We also explore an extension of our results to scalar fields minimally coupled to an electromagnetic field.     

Colored scalar in a chromomagnetic field

The motion of colored scalar particles in a constant color magnetic field is considered. The Klein-Gordon equation is solved in this background and the energy spectrum is quantized by boundary conditions. The unitary transformation diagonalizing this equation and the states with definite energy are found.     

A Consistency Check for the Free Scalar Field Theory Realization of the Doubly Spacial Relativity *

We study a free scalar field theory in the framework of the Magueijo-Smolin model of the "Doubly Special Relativity" (DSR) which is a non-linear realization of the action of the Lorentz group on momentum space admitting an invariant energy cutoff. We show that unlike the standard quantum field theory, the Klein-Gordon equation obtained via Euler-Lagrange field equation and Heisenberg picture equation of motion of the field are not equivalent in this framework, at least up to the first order of the Planck length scale.     

Creation of boson pairs from vacuum

A general theory is derived for the creation of pairs of spinless particles from vacuum in the presence of an electromagnetic field. If the exact solutions of the Klein-Gordon equation are known for the particle in the given external field, the pair-creation problem can be solved.     

库仑势加新环形势的相对论束缚态

在标量势等于矢量势的条件下，获得了库仑势加新环形势的Klein-Gordon方程和Dirac方程的束缚态的精确解. 对于Klein-Gordon方程，获得了精确的能谱方程和归一化的波函数. 对于Dirac方程，给出了精确的能谱方程和归一化的旋量波函数. 关键词： 库仑势加新环形势 束缚态 精确解     

The dynamical behavior of scalar fields near the initial singularity

Analyzing the Klein-Gordon equation in a homogeneous, Isotropic and spatially flat universe model, we find the conditions for the existence of a universe dominated by a scalar field in its early stages.