scholarly journals The N- and 1-Time Classical Descriptions of N-Body Relativistic Kinematics and the Electromagnetic Interaction

1997 ◽  
Vol 12 (04) ◽  
pp. 645-722 ◽  
Author(s):  
Luca Lusanna
Keyword(s):  
Electromagnetic Field ◽  
Hamiltonian Formulation ◽  
Covariant Formulation ◽  
Coulomb Interactions ◽  
Charged Scalar ◽  
Scalar Particles ◽  
Dimensional Phase Space ◽  
Spacelike Hypersurfaces ◽  
Klein Gordon ◽  
Time Description

Given N relativistic scalar free particles described by N mass-shell first class constraints in their 8N-dimensional phase space, their N-time description is obtained by means of a series of canonical transformations to a quasi-Shanmugadhasan basis adapted to the constraints. Then the same system is reformulated on spacelike hypersurfaces: the restriction to the family of hyperplanes orthogonal to the total timelike momentum gives rise to a covariant intrinsic 1-time formulation called the "rest-frame instant form" of dynamics. The relation between the N- and 1-time descriptions, the mass spectrum of the system and the way to introduce mutual interactions among the particles are studied. Then the 1-time description of the isolated system of N charged scalar particles plus the electromagnetic field is obtained. The use of Grassmann variables to describe the charges together with the determination of the field and particle Dirac observables leads to a formulation without infinite self-energies and with mutual Coulomb interactions extracted from classical electromagnetic field theory. A comparison with the Feshbach–Villars Hamiltonian formulation of the Klein–Gordon equation is made. Finally a 1-time covariant formulation of relativistic statistical mechanics is found.

scholarly journals THE LIENARD–WIECHERT POTENTIAL OF CHARGED SCALAR PARTICLES AND THEIR RELATION TO SCALAR ELECTRODYNAMICS IN THE REST-FRAME INSTANT FORM

1998 ◽  
Vol 13 (16) ◽  
pp. 2791-2831 ◽  
Author(s):  
DAVID ALBA ◽  
LUCA LUSANNA
Keyword(s):  
Electromagnetic Field ◽  
Dirac Equation ◽  
Rest Frame ◽  
Coulomb Gauge ◽  
Charged Scalar ◽  
Scalar Particles ◽  
Field System ◽  
Instant Form ◽  
Hamilton Equations ◽  
New Type

After a summary of a recently proposed new type of instant form of dynamics (the Wigner-covariant rest-frame instant form), the reduced Hamilton equations in the covariant rest-frame Coulomb gauge for the isolated system of N scalar particles with pseudoclassical Grassmann-valued electric charges plus the electromagnetic field are studied. The Lienard–Wiechert potentials of the particles are evaluated and it is shown how the causality problems of the Abraham–Lorentz–Dirac equation are solved at the pseudoclassical level. Then, the covariant rest-frame description of scalar electrodynamics is given. Applying to it the Feshbach–Villars formalism, the connection with the particle plus electromagnetic field system is found.

scholarly journals Noninertial effects on a scalar field in a spacetime with a magnetic screw dislocation

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Ricardo L. L. Vitória
Keyword(s):  
Scalar Field ◽  
Screw Dislocation ◽  
Bound States ◽  
Charged Scalar ◽  
Wall Potential ◽  
Noninertial Effects ◽  
Klein Gordon ◽  
Coulomb Type ◽  
Charged Scalar Field ◽  
Type Potential

Abstract We investigate rotating effects on a charged scalar field immersed in spacetime with a magnetic screw dislocation. In addition to the hard-wall potential, which we impose to satisfy a boundary condition from the rotating effect, we insert a Coulomb-type potential and the Klein–Gordon oscillator into this system, where, analytically, we obtain solutions of bound states which are influenced not only by the spacetime topology, but also by the rotating effects, as a Sagnac-type effect modified by the presence of the magnetic screw dislocation.

Mechanics of a charged particle on the Kaluza–Klein background

1995 ◽  
Vol 73 (9-10) ◽  
pp. 602-607 ◽  
Author(s):  
S. R. Vatsya
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Integral Method ◽  
Gordon Equation ◽  
Type Equation ◽  
Fifth Dimension ◽  
Klein Gordon ◽  
Path Integral Method ◽  
Klein Gordon Equation ◽  
Kaluza Klein

The path-integral method is used to derive a generalized Schrödinger-type equation from the Kaluza–Klein Lagrangian for a charged particle in an electromagnetic field. The compactness of the fifth dimension and the properties of the physical paths are used to decompose this equation into its infinite components, one of them being similar to the Klein–Gordon equation.

SOLITARY WAVES OF THE NONLINEAR KLEIN-GORDON EQUATION COUPLED WITH THE MAXWELL EQUATIONS

2002 ◽  
Vol 14 (04) ◽  
pp. 409-420 ◽  
Author(s):  
VIERI BENCI ◽  
DONATO FORTUNATO FORTUNATO
Keyword(s):  
Electromagnetic Field ◽  
Solitary Wave ◽  
Electric Field ◽  
Solitary Waves ◽  
Maxwell Equations ◽  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation

This paper is divided in two parts. In the first part we construct a model which describes solitary waves of the nonlinear Klein-Gordon equation interacting with the electromagnetic field. In the second part we study the electrostatic case. We prove the existence of infinitely many pairs (ψ, E), where ψ is a solitary wave for the nonlinear Klein-Gordon equation and E is the electric field related to ψ.

Electromagnetic interaction with the Klein–Gordon equation in the framework of GUP

2021 ◽  
Vol 18 (12) ◽  
Author(s):  
B. Khosropour
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Uncertainty Principle ◽  
Electric Potential ◽  
Uniform Magnetic Field ◽  
Gordon Equation ◽  
Electromagnetic Interaction ◽  
Generalized Uncertainty Principle ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this work, according to the generalized uncertainty principle, we study the Klein–Gordon equation interacting with the electromagnetic field. The generalized Klein–Gordon equation is obtained in the presence of a scalar electric potential and a uniform magnetic field. Furthermore, we find the relation of the generalized energy–momentum in the presence of a scalar electric potential and a uniform magnetic field separately.

scholarly journals ON THE CREATION OF SCALAR PARTICLES IN A FLAT ROBERTSON–WALKER SPACETIME

2011 ◽  
Vol 26 (35) ◽  
pp. 2639-2651 ◽  
Author(s):  
S. HAOUAT ◽  
R. CHEKIREB
Keyword(s):  
Exact Solutions ◽  
Effective Action ◽  
Gordon Equation ◽  
Transition Probability ◽  
Particle Creation ◽  
Pair Creation ◽  
Bogoliubov Transformation ◽  
Scalar Particles ◽  
Klein Gordon ◽  
Klein Gordon Equation

The problem of particle creation from vacuum in a flat Robertson–Walker spacetime is studied. Two sets of exact solutions for the Klein–Gordon equation are given when the scale factor is a2(η) = a+b tanh(λη)+c tanh2 (λη). Then the canonical method based on Bogoliubov transformation is applied to calculate the pair creation probability and the density number of created particles. Some particular cosmological models such as radiation dominated universe and Milne universe are discussed. For both cases the vacuum to vacuum transition probability is calculated and the imaginary part of the effective action is extracted.

scholarly journals Quantum states of an electromagnetic field interacting with a classical current and their applications to radiation problems

2020 ◽  
Vol 27 (4) ◽  
pp. 902-911
Author(s):  
V. G. Bagrov ◽  
D. M. Gitman ◽  
A. A. Shishmarev ◽  
A. J. D. Farias
Keyword(s):  
Electromagnetic Field ◽  
Synchrotron Radiation ◽  
Dirac Equation ◽  
Photon Emission ◽  
Quantum States ◽  
Photon Radiation ◽  
Electric Currents ◽  
Scalar Particles ◽  
Two Photon ◽  
The Relationship

Synchrotron radiation was originally studied by classical methods using the Liénard–Wiechert potentials of electric currents. Subsequently, quantum corrections to the classical formulas were studied, considering the emission of photons arising from electronic transitions between spectral levels, described in terms of the Dirac equation. In this paper, an intermediate approach is considered, in which electric currents generating the radiation are considered classically while the quantum nature of the radiation is taken into account exactly. Such an approximate approach may be helpful in some cases; it allows one to study one-photon and multi-photon radiation without complicating calculations using corresponding solutions of the Dirac equation. Here, exact quantum states of an electromagnetic field interacting with classical currents are constructed and their properties studied. With their help, the probability of photon emission by classical currents is calculated and relatively simple formulas for one-photon and multi-photon radiation are obtained. Using the specific circular electric current, the corresponding synchrotron radiation is calculated. The relationship between the obtained results and those known before are discussed, for example with the Schott formula, with Schwinger calculations, with one-photon radiation of scalar particles due to transitions between Landau levels, and with some previous results of calculating two-photon synchrotron radiation.

scholarly journals Supplying dark energy from scalar field dark matter

2018 ◽  
Vol 27 (09) ◽  
pp. 1850100
Author(s):  
Merab Gogberashvili ◽  
Alexander Sakharov
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Gordon Equation ◽  
Einstein Condensate ◽  
Scalar Particles ◽  
Bose Einstein Condensate ◽  
Constant Solution ◽  
Klein Gordon ◽  
Free Parameters ◽  
Bose Einstein

We consider the hypothesis that dark matter (DM) and dark energy (DE) consist of ultra-light self-interacting scalar particles. It is found that the Klein–Gordon equation with only two free parameters (mass and self-coupling) on a Schwarzschild background, at the galactic length-scales has the solution which corresponds to Bose–Einstein Condensate (BEC), behaving as DM, while the constant solution at supra-galactic scales can explain DE.

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