scholarly journals A Finite and Discrete Model for Single Fermion Mass Renormalization: Derivation of the Free Particle Dirac Equation

1995 ◽  
Vol 8 (3) ◽  
pp. 434-445 ◽  
Author(s):  
H. Pierre Noyes
Keyword(s):  
Dirac Equation ◽  
Discrete Model ◽  
Free Particle ◽  
Fermion Mass ◽  
Mass Renormalization

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.

scholarly journals Quantum backflow in solutions to the Dirac equation of the spin-1 2 free particle

2018 ◽  
Vol 33 (32) ◽  
pp. 1850186 ◽  
Author(s):  
Hong-Yi Su ◽  
Jing-Ling Chen
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Relativistic Particle ◽  
Relativistic Quantum ◽  
Free Particle ◽  
Negative Energy ◽  
Dirac Particle ◽  
Relativistic Quantum Mechanics ◽  
Probability Current ◽  
Negative Probability

It was known that a free, non-relativistic particle in a superposition of positive momenta can, in certain cases, bear a negative probability current — hence termed quantum backflow. Here, it is shown that more variations can be brought about for a free Dirac particle, particularly when negative-energy solutions are taken into account. Since any Dirac particle can be understood as an antiparticle that acts oppositely (and vice versa), quantum backflow is found to arise in the superposition (i) of a well-defined momentum but different signs of energies, or more remarkably (ii) of different signs of both momenta and energies. Neither of these cases has a counterpart in non-relativistic quantum mechanics. A generalization by using the field-theoretic formalism is also presented and discussed.

GAUGE DEPENDENCE OF FERMION MASS RENORMALIZATION PRESCRIPTIONS

2009 ◽  
Vol 24 (04) ◽  
pp. 291-304
Author(s):  
YONG ZHOU
Keyword(s):  
Fermion Mass ◽  
Pole Mass ◽  
Mass Renormalization ◽  
Gauge Dependence ◽  
Loop Level ◽  
The Difference ◽  
First Time ◽  
Level Calculation ◽  
Physical Result ◽  
Mass Definition

We discuss the gauge dependence of fermion mass definition under the on-shell and pole mass renormalization prescriptions. By the two-loop-level calculation of the cross section of the physical process [Formula: see text], we prove for the first time that the on-shell fermion mass renormalization prescription makes physical result gauge-dependent. On the other hand, such gauge dependence does not appear in the result of the pole mass renormalization prescription. Our calculation also implies that the difference of physical results between the two mass renormalization prescriptions cannot be neglected at two-loop level.

scholarly journals Position-dependent mass Dirac equation and local Fermi velocity

2021 ◽  
Author(s):  
Rahul Ghosh
Keyword(s):  
Dirac Equation ◽  
Free Particle ◽  
Quadratic Functional ◽  
Fermi Velocity ◽  
New Approach ◽  
Coupled Equations ◽  
The One ◽  
Dependent Mass ◽  
Local Variable ◽  
Position Dependent Mass

Abstract We present a new approach to study the one-dimensional Dirac equation in the background of a position-dependent mass m. Taking the Fermi velocity vf to be a local variable, we explore the resulting structure of the coupled equations and arrive at an interesting constraint of m turning out to be the inverse square of vf. We address several solvable systems that include the free particle, shifted harmonic oscillator, Coulomb and nonpolynomial potentials. In particular, in the supersymmetric quantum mechanics context, the upper partner of the effective potential yields a new form for an inverse quadratic functional choice of the Fermi velocity.

scholarly journals QUANTUM STATE OF A FREE SPIN-½ PARTICLE AND THE INEXTRICABLE DEPENDENCE OF SPIN AND MOMENTUM UNDER LORENTZ TRANSFORMATIONS

2012 ◽  
Vol 10 (04) ◽  
pp. 1230003 ◽  
Author(s):  
TIAGO DEBARBA ◽  
REINALDO O. VIANNA
Keyword(s):  
Dirac Equation ◽  
Quantum State ◽  
Free Particle ◽  
Lorentz Transformations ◽  
Spin Particle ◽  
Quantization Axis ◽  
Spin Quantization

We revise the Dirac equation for a free particle and investigate Lorentz transformations on spinors. We study how the spin quantization axis changes under Lorentz transformations, and evince the interplay between spin and momentum in this context.

Quaternionic Dirac free particle

2021 ◽  
Author(s):  
Sergio Giardino
Keyword(s):  
Field Theory ◽  
Dirac Equation ◽  
Real Hilbert Space ◽  
Free Particle ◽  
Massive Particle ◽  
Essential Element ◽  
Massless Particle ◽  
Quantum Field ◽  
Quaternionic Quantum Mechanics ◽  
Theory Formula

In this paper, we solve the quaternionic Dirac equation [Formula: see text] in the real Hilbert space, and we ascertain that their free particle solutions set comprises eight elements in the case of a massive particle, and a four elements solutions set in the case of a massless particle, a richer situation when compared to the four elements solutions set of the usual complex Dirac equation [Formula: see text]. These free particle solutions were unknown in the previous solutions of anti-Hermitian quaternionic quantum mechanics, and constitute an essential element in order to build a quaternionic quantum field theory [Formula: see text].

Notizen:Eichfeldtheorie zur U3-invarianten Pais-Gleichung/ Gauge Field Theory of an U3-invariant Pais Equation

1980 ◽  
Vol 35 (3) ◽  
pp. 355-357
Author(s):  
Fritz Bopp
Keyword(s):  
Field Theory ◽  
Dirac Equation ◽  
Gauge Field ◽  
Free Particle ◽  
Gauge Field Theory

AbstractWe are looking for the gauge field theory which corresponds to the U3-invariance of the recently obtained free particle Dirac equation generalized according to an idea of Pais.

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