Nonuniqueness of the Lorentz-Dirac equation with the free-particle asymptotic condition

1995 ◽  
Vol 51 (1) ◽  
pp. 680-689 ◽  
Author(s):  
R. Blanco
Keyword(s):  
Dirac Equation ◽  
Free Particle ◽  
Asymptotic Condition

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.

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.

scholarly journals Charge Conjugation Symmetry in the Finite Basis Approximation of the Dirac Equation

2020 ◽  
Author(s):  
Maen Salman ◽  
Trond Saue
Keyword(s):  
Angular Momentum ◽  
Dirac Equation ◽  
Free Particle ◽  
Finite Basis ◽  
Basis Functions ◽  
Charge Conjugation ◽  
Basis Set ◽  
Basis Sets ◽  
Pair Approximation ◽  
Central Field

4-component relativistic atomic and molecular calculations are typically performed within the no-pair approximation where negative-energy solutions are discarded, hence the symmetry between electronic and positronic solutions is not considered. These states are however needed in QED calculations, where furthermore charge conjugation symmetry becomes an issue. In this work we shall discuss the realization of charge conjugation symmetry of the Dirac equation in a central field within the finite basis approximation. Three schemes for basis set construction are considered: restricted, inverse and dual kinetic balance. We find that charge conjugation symmetry can be realized within the restricted and inverse kinetic balance prescriptions, but only with a special form of basis functions that does not obey the right boundary conditions of the radial wavefunctions. The dual kinetic balance prescription is on the other hand compatible with charge conjugation symmetry without restricting the form of the radial basis functions. However, since charge conjugation relates solutions of opposite value of the quantum number κ, this requires the use of basis sets chosen according to total angular momentum j rather than orbital angular momentum ` . As a special case, we consider the free-particle Dirac equation, where the solutions of opposite sign of energy are related by charge conjugation symmetry. We note that there is additional symmetry in those solutions of the same value of κ come in pairs of opposite energy.

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