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 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.

The Einstein–Maxwell-particle system in the York canonical basis of ADM tetrad gravity. Part 1. The equations of motion in arbitrary Schwinger time gauges 1This paper is one of three companion papers published in the same issue of Can. J. Phys.

2012 ◽  
Vol 90 (11) ◽  
pp. 1017-1076 ◽  
Author(s):  
David Alba ◽  
Luca Lusanna
Keyword(s):  
Electromagnetic Field ◽  
Particle System ◽  
Canonical Basis ◽  
Kinetic Term ◽  
Back Reaction ◽  
Special Role ◽  
Charged Scalar ◽  
Hamilton Equations ◽  
Tetrad Gravity ◽  
Transverse Electromagnetic

We study the coupling of N charged scalar particles plus the electromagnetic field to Arnowitt–Deser–Misner (ADM) tetrad gravity and its canonical formulation in asymptotically Minkowskian space–times without super-translations. To regularize the self-energies, both the electric charge and the sign of the energy of the particles are Grassmann-valued. The introduction of the noncovariant radiation gauge allows reformulation of the theory in terms of transverse electromagnetic fields and to extract the generalization of the Coulomb interaction among the particles in the riemannian instantaneous 3-spaces of global noninertial frames, the only ones allowed by the equivalence principle. Then we make the canonical transformation to the York canonical basis, where there is a separation between the inertial (gauge) variables and the tidal ones inside the gravitational field and a special role of the eulerian observers associated with the 3+1 splitting of space–time. The Dirac hamiltonian is weakly equal to the weak ADM energy. The Hamilton equations in Schwinger time gauges are given explicitly. In the York basis they are naturally divided into four sets: (i) the contracted Bianchi identities; (ii) the equations for the inertial gauge variables; (iii) the equations for the tidal ones; and (iv) the equations for matter. Finally, we give the restriction of the Hamilton equations and of the constraints to the family of nonharmonic 3-orthogonal gauges, in which the instantaneous riemannian 3-spaces have a nonfixed trace 3K of the extrinsic curvature but a diagonal 3-metric. The inertial gauge variable 3K (the general-relativistic remnant of the freedom in the clock synchronization convention) gives rise to a negative kinetic term in the weak ADM energy vanishing only in the gauges with 3K = 0: is it relevant for dark energy and back-reaction? In the second paper will appear the linearization of the theory in these nonharmonic 3-orthogonal gauges to obtain hamiltonian post-minkowskian gravity (without post-newtonian approximations) with asymptotic Minkowski background, nonflat instantaneous 3-spaces and no post-newtonian expansion. This will allow the exploration of the inertial effects induced by the York time 3K in nonflat 3-spaces (they do not exist in newtonian gravity) and to check how well dark matter can be explained as an inertial aspect of Einstein’s general relativity: this will be done in a third paper on the post-minkowskian 2-body problem in the absence of the electromagnetic field and on its 0.5 post-newtonian limit.

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 Time evolution of the free Dirac field in spatially flat FLRW space–times

2020 ◽  
Vol 35 (32) ◽  
pp. 2030019
Author(s):  
Ion I. Cotăescu
Keyword(s):  
Dirac Equation ◽  
Rest Frame ◽  
Relativistic Quantum ◽  
Fundamental Solutions ◽  
Relativistic Quantum Mechanics ◽  
Dirac Field ◽  
De Sitter ◽  
Spherical Waves ◽  
New Type ◽  
First Time

The framework of the relativistic quantum mechanics on spatially flat FLRW space–times is considered for deriving the analytical solutions of the Dirac equation in different local charts of these manifolds. Systems of commuting conserved operators are used for determining the fundamental solutions as common eigenspinors giving thus physical meaning to the integration constants related to the eigenvalues of these operators. Since these systems, in general, are incomplete on the FLRW space–times there are integration constants that must be fixed by setting the vacuum either as the traditional adiabatic one or as the rest frame vacuum we proposed recently. All the known solutions of the Dirac equation on these manifolds are discussed in all details and a new type of spherical waves of given energy in the de Sitter expanding universe is reported here for the first time.

scholarly journals Towards relativistic atomic physics. Part II. Collective and relative relativistic variables for a system of charged articles plus the electromagnetic field

2010 ◽  
Vol 88 (6) ◽  
pp. 425-463 ◽  
Author(s):  
David Alba ◽  
Horace W. Crater ◽  
Luca Lusanna
Keyword(s):  
Electromagnetic Field ◽  
Coulomb Interaction ◽  
Atomic Physics ◽  
Electric Dipole ◽  
Rest Frame ◽  
Charged Particles ◽  
Collective Variable ◽  
Positive Energy ◽  
Instant Form ◽  
Transverse Electromagnetic

In this second paper, we complete the classical description of an isolated system of “charged positive-energy particles, with Grassmann-valued electric charges and mutual Coulomb interaction, plus a transverse electromagnetic field” in the rest-frame instant form of dynamics. In particular, we show how to determine a collective variable associated with the internal 3-center of mass on the instantaneous 3-spaces, to be eliminated with the constraints [Formula: see text]. Here, [Formula: see text] is the Lorentz boost generator in the unfaithful internal realization of the Poincaré group and its vanishing is the gauge-fixing to the rest-frame conditions [Formula: see text]. We show how to find this collective variable for the following isolated systems: (a) charged particles with a Coulomb plus Darwin mutual interaction; (b) transverse radiation field; (c) charged particles with a mutual Coulomb interaction plus a transverse electro-magnetic field. Then we define the Dixon multipolar expansion for the open particle subsystem. We also define the relativistic electric dipole approximation of atomic physics in the rest-frame instant form and we find a possible relativistic generalization of the electric dipole representation.

scholarly journals THE SEMICLASSICAL RELATIVISTIC DARWIN POTENTIAL FOR SPINNING PARTICLES IN THE REST-FRAME INSTANT FORM: TWO-BODY BOUND STATES WITH SPIN 1/2 CONSTITUENTS

2001 ◽  
Vol 16 (20) ◽  
pp. 3365-3477 ◽  
Author(s):  
DAVID ALBA ◽  
HORACE CRATER ◽  
LUCA LUSANNA
Keyword(s):  
Bound States ◽  
Rest Frame ◽  
Semiclassical Approximation ◽  
Positive Energy ◽  
Standard Result ◽  
Spinning Particles ◽  
Arbitrary Mass ◽  
Scalar Particles ◽  
Instant Form ◽  
Interparticle Potential

We extend previous results on the extraction of the Darwin potential to all orders in c-2 from the radiation gauge Lienard–Wiechert solution for the system of N positive-energy scalar particles plus the electromagnetic field in the Wigner-covariant rest-frame instant form of dynamics to the case of N positive-energy spinning particles. This is done in the semiclassical approximation of using Grassmann-valued electric charges for regularizing the Coulomb self-energies and extracting the unique semiclassical action-at-a-distance interaction hidden in any Green function used for the Lienard–Wiechert solution. By describing semiclassically also the spin of the particles with Grassmann variables, by means of a semiclassical Foldy–Wouthuysen transformation applied the the Dirac-like constraints of the manifestly Lorentz covariant spinning particles, we determine the coupling of positive-energy spinning particles to the electric field in the semiclassical approximation. Then we follow the same procedure developed for scalar particles and, in the sector where there is no in-radiation, we determine the effective semiclassical interparticle potential. Besides the relativistic Darwin term there are spin-orbit and spin-spin terms in the potential. Quantization of the lowest order (in c-2) part of the closed form of the effective Hamiltonian in the case N = 2 reproduces exactly the standard result of the reduction of the Bethe–Salpeter equation for the bound states of two spin 1/2 constituents of arbitrary mass (hydrogen atom, positronium, muonium).

scholarly journals The Dirac Electron Consistent with Proper Gravitational and Electromagnetic Field of the Kerr–Newman Solution

Galaxies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 18
Author(s):  
Alexander Burinskii
Keyword(s):  
Electromagnetic Field ◽  
Quantum Theory ◽  
Gravitational Field ◽  
Dirac Equation ◽  
Higgs Field ◽  
Vacuum State ◽  
Relativistic String ◽  
Dirac Equations ◽  
Dirac Electron ◽  
Relativistic Scattering

The Dirac electron is considered as a particle-like solution consistent with its own Kerr–Newman (KN) gravitational field. In our previous works we considered the regularized by López KN solution as a bag-like soliton model formed from the Higgs field in a supersymmetric vacuum state. This bag takes the shape of a thin superconducting disk coupled with circular string placed along its perimeter. Using the unique features of the Kerr–Schild coordinate system, which linearizes Dirac equation in KN space, we obtain the solution of the Dirac equations consistent with the KN gravitational and electromagnetic field, and show that the corresponding solution takes the form of a massless relativistic string. Obvious parallelism with Heisenberg and Schrödinger pictures of quantum theory explains remarkable features of the electron in its interaction with gravity and in the relativistic scattering processes.

The Einstein–Maxwell-particle system in the York canonical basis of ADM tetrad gravity. Part 2. The weak field approximation in the 3-orthogonal gauges and Hamiltonian post-minkowskian gravity: the N-body problem and gravitational waves with asymptotic background 1This paper is one of three companion papers published in the same issue of Can. J. Phys.

2012 ◽  
Vol 90 (11) ◽  
pp. 1077-1130 ◽  
Author(s):  
David Alba ◽  
Luca Lusanna
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Waves ◽  
Particle System ◽  
Canonical Basis ◽  
Field Approximation ◽  
Weak Field ◽  
N Body Problem ◽  
Hamilton Equations ◽  
Weak Field Approximation ◽  
Tetrad Gravity

In this second paper we define a post-minkowskian (PM) weak field approximation leading to a linearization of the Hamilton equations of Arnowitt–Deser–Misner (ADM) tetrad gravity in the York canonical basis in a family of nonharmonic 3-orthogonal Schwinger time gauges. The York time 3K (the relativistic inertial gauge variable, not existing in newtonian gravity, parametrizing the family, and connected to the freedom in clock synchronization, i.e., to the definition of the the shape of the instantaneous 3-spaces) is set equal to an arbitrary numerical function. The matter are considered point particles, with a Grassmann regularization of self-energies, and the electromagnetic field in the radiation gauge: an ultraviolet cutoff allows a consistent linearization, which is shown to be the lowest order of a hamiltonian PM expansion. We solve the constraints and the Hamilton equations for the tidal variables and we find PM gravitational waves with asymptotic background (and the correct quadrupole emission formula) propagating on dynamically determined non-euclidean 3-spaces. The conserved ADM energy and the Grassmann regularization of self-energies imply the correct energy balance. A generalized transverse–traceless gauge can be identified and the main tools for the detection of gravitational waves are reproduced in these nonharmonic gauges. In conclusion, we get a PM solution for the gravitational field and we identify a class of PM Einstein space–times, which will be studied in more detail in a third paper together with the PM equations of motion for the particles and their post-newtonian expansion (but in the absence of the electromagnetic field). Finally we make a discussion on the gauge problem in general relativity to understand which type of experimental observations may lead to a preferred choice for the inertial gauge variable 3K in PM space–times. In the third paper we will show that this choice is connected with the problem of dark matter.

Sign in / Sign up

Export Citation Format

Share Document