A Covariant Semi-Classical Theory of the Radiating Electron

1977 ◽  
Vol 32 (1) ◽  
pp. 101-102
Author(s):  
M. Sorg
Keyword(s):  
Classical Theory ◽  
Characteristic Length ◽  
Order Approximation ◽  
Classical Equation ◽  
Radiation Reaction ◽  
Equation Of Motion ◽  
Compton Wavelength ◽  
Classical Electron ◽  
Electron Radius ◽  
Classical Electron Radius

Abstract A new semi-classical equation of motion is suggested for the radiating electron. The characteristic length of the new theory is the Compton wavelength λc(= ħ/2 m c) instead of the classical electron radius which is used in all purely classical theories of the radiating electron. However, the lowest order approximation of the radiation reaction contains only the classical radius rc.

scholarly journals The Abraham–Lorentz force and electrodynamics at the classical electron radius

2019 ◽  
Vol 34 (15) ◽  
pp. 1950077 ◽  
Author(s):  
Janos Polonyi
Keyword(s):  
Lorentz Force ◽  
Radiation Reaction ◽  
Classical Electron ◽  
Satisfactory Description ◽  
Point Splitting ◽  
Reaction Forces ◽  
Electron Radius ◽  
Classical Language ◽  
Classical Electron Radius ◽  
Classical Radiation

The Abraham–Lorentz force is a finite remnant of the UV singular structure of the self-interaction of a point charge with its own field. The satisfactory description of such an interaction needs a relativistic regulator. This turns out to be a problematic point because the energy of regulated relativistic cutoff theories is unbounded from below. However, one can construct point-splitting regulators which keep the Abraham–Lorentz force stable. The classical language can be reconciled with QED by pointing out that the effective quantum theory for the electric charge supports a saddle point producing the classical radiation reaction forces.

Interacting charges and the classical electron radius

2018 ◽  
Vol 39 (2) ◽  
pp. 025706
Author(s):  
Roberto De Luca ◽  
Marco Di Mauro ◽  
Orazio Faella ◽  
Adele Naddeo
Keyword(s):  
Classical Electron ◽  
Electron Radius ◽  
Classical Electron Radius

Coherent states, Schrödinger equation, and the Hamilton–Jacobi equation

1995 ◽  
Vol 73 (7-8) ◽  
pp. 478-483
Author(s):  
Rachad M. Shoucri
Keyword(s):  
Schrödinger Equation ◽  
Jacobi Equation ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Hidden Variables ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Phase Variable ◽  
Independent Variable ◽  
Hamilton Jacobi Equation

The self-adjoint form of the classical equation of motion of the harmonic oscillator is used to derive a Hamiltonian-like equation and the Schrödinger equation in quantum mechanics. A phase variable ϕ(t) instead of time t is used as an independent variable. It is shown that the Hamilton–Jacobi solution in this case is identical with the solution obtained from the Schrödinger equation without the need to introduce the idea of hidden variables or quantum potential.

Classical, Covariant Finite-size Model of the Radiating Electron

1974 ◽  
Vol 29 (11) ◽  
pp. 1671-1684 ◽  
Author(s):  
M. Sorg
Keyword(s):  
Dirac Equation ◽  
Finite Size ◽  
Finite Extension ◽  
Equation Of Motion ◽  
Mass Renormalization ◽  
Classical Electron ◽  
Size Model

The finite extension of the classical electron is defined in a new, covariant manner. This new definition enables one to calculate exactly the bound and emitted four-momentum and to find an equation of motion different from the Lorentz-Dirac equation and from other equations proposed in the literature. Neither mass renormalization nor use of advanced quantities nor asymptotic conditions are necessary. Runaway solutions and pre-acceleration do not occur in the framework of the model presented here.

Coherent states and geometric phases of a generalized damped harmonic oscillator with time-dependent mass and frequency

2014 ◽  
Vol 28 (26) ◽  
pp. 1450177 ◽  
Author(s):  
I. A. Pedrosa ◽  
D. A. P. de Lima
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Quantum Invariant ◽  
Dynamical Phase ◽  
Special Cases ◽  
Berry Phases ◽  
Dependent Mass

In this paper, we study the generalized harmonic oscillator with arbitrary time-dependent mass and frequency subjected to a linear velocity-dependent frictional force from classical and quantum points of view. We obtain the solution of the classical equation of motion of this system for some particular cases and derive an equation of motion that describes three different systems. Furthermore, with the help of the quantum invariant method and using quadratic invariants we solve analytically and exactly the time-dependent Schrödinger equation for this system. Afterwards, we construct coherent states for the quantized system and employ them to investigate some of the system's quantum properties such as quantum fluctuations of the coordinate and the momentum as well as the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary system. Finally, we evaluate the dynamical and Berry phases for three special cases and surprisingly find identical expressions for the dynamical phase and the same formulae for the Berry's phase.

Equation of motion with gravitational radiation

2014 ◽  
Vol 23 (12) ◽  
pp. 1442010
Author(s):  
Richard T. Hammond
Keyword(s):  
Gravitational Radiation ◽  
Minkowski Spacetime ◽  
Radiation Reaction ◽  
Equation Of Motion ◽  
Electrodynamic Problem ◽  
New Approach ◽  
Successful Solution

A new approach to gravitational radiation reaction is developed which is generalized from a successful solution to the electrodynamic problem in Minkowski spacetime.

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