Quantum Minkowski Space and the q -Analogue of Dirac Equation

1992 ◽  
Vol 18 (2) ◽  
pp. 199-206
Author(s):  
Xing-Chang Song
Keyword(s):  
Dirac Equation ◽  
Minkowski Space

scholarly journals Nature itself in a mirror space–time

2015 ◽  
Vol 93 (10) ◽  
pp. 1005-1008 ◽  
Author(s):  
Rasulkhozha S. Sharafiddinov
Keyword(s):  
Dirac Equation ◽  
Minkowski Space ◽  
Space Time ◽  
Point Of View ◽  
Classical Solutions ◽  
Left Handed ◽  
Minkowski Space Time ◽  
Energy And Momentum ◽  
The Right ◽  
Structure Of Matter

The unity of the structure of matter fields with flavor symmetry laws involves that the left-handed neutrino in the field of emission can be converted into a right-handed one and vice versa. These transitions together with classical solutions of the Dirac equation testify in favor of the unidenticality of masses, energies, and momenta of neutrinos of the different components. If we recognize such a difference in masses, energies, and momenta, accepting its ideas about that the left-handed neutrino and the right-handed antineutrino refer to long-lived leptons, and the right-handed neutrino and the left-handed antineutrino are short-lived fermions, we would follow the mathematical logic of the Dirac equation in the presence of the flavor symmetrical mass, energy, and momentum matrices. From their point of view, nature itself separates Minkowski space into left and right spaces concerning a certain middle dynamical line. Thereby, it characterizes any Dirac particle both by left and by right space–time coordinates. It is not excluded therefore that whatever the main purposes each of earlier experiments about sterile neutrinos, namely, about right-handed short-lived neutrinos may serve as the source of facts confirming the existence of a mirror Minkowski space–time.

scholarly journals THE DIRAC–HESTENES EQUATION FOR SPHERICAL SYMMETRIC POTENTIALS IN THE SPHERICAL AND CARTESIAN GAUGES

2006 ◽  
Vol 21 (19n20) ◽  
pp. 4071-4082 ◽  
Author(s):  
ROLDÃO DA ROCHA ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Dirac Equation ◽  
Minkowski Space ◽  
Spherical Symmetry ◽  
Separation Of Variables ◽  
Differential Forms ◽  
Space Time ◽  
Minkowski Space Time ◽  
Clifford Bundle

In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space–time the Dirac–Hestenes equation — which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation — by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac–Hestenes equation in both gauges has exactly the same mathematical difficulty.

The Lorentz–Dirac equation in Minkowski space

1994 ◽  
Vol 35 (7) ◽  
pp. 3482-3489 ◽  
Author(s):  
Violeta Gaftoi ◽  
José L. López‐Bonilla ◽  
Jesús Morales ◽  
Marco A. Rosales
Keyword(s):  
Dirac Equation ◽  
Minkowski Space

scholarly journals Chiral symmetry breaking as a geometrical process

2014 ◽  
Vol 29 (26) ◽  
pp. 1450145 ◽  
Author(s):  
E. Bittencourt ◽  
S. Faci ◽  
M. Novello
Keyword(s):  
Dirac Equation ◽  
Symmetry Breaking ◽  
Minkowski Space ◽  
Chiral Symmetry ◽  
Spinor Field ◽  
Chiral Symmetry Breaking ◽  
Curved Space ◽  
Left Handed ◽  
Chiral Component ◽  
The Right

This paper is an extension for spinor fields the recently developed Dynamical Bridge formalism which relates a linear dynamics in a curved space to a nonlinear dynamics in Minkowski space. This leads to a new geometrical mechanism to generate a chiral symmetry breaking without mass, providing an alternative explanation for the absence of right-handed neutrinos. We analyze a spinor field obeying the Dirac equation in a curved space which is constructed by its own current. This way, both chiralities of the spinor field satisfy the same dynamics in the curved space. Afterward, the dynamical equation is re-expressed in terms of the flat Minkowski space and then each chiral component behaves differently. The left-handed part of the spinor field satisfies the Dirac equation while the right-handed part is trapped by a Nambu–Jona-Lasinio type potential.

Symmetries of the massless Dirac equation in Minkowski space

1988 ◽  
Vol 38 (12) ◽  
pp. 3837-3839 ◽  
Author(s):  
Stéphane Durand ◽  
Jean-Marc Lina ◽  
Luc Vinet
Keyword(s):  
Dirac Equation ◽  
Minkowski Space

scholarly journals Dirac Particles in the Minkowski Space with Torsion

1978 ◽  
Vol 31 (2) ◽  
pp. 195 ◽  
Author(s):  
MP O'Connor ◽  
PK Smrz
Keyword(s):  
Dirac Equation ◽  
Minkowski Space ◽  
Covariant Derivative ◽  
Dirac Spinor ◽  
Simple Derivation ◽  
Minkowski Metric ◽  
Dirac Particles ◽  
Straight Line ◽  
Constant Torsion

After presenting a simple derivation of the covariant derivative of the Dirac spinor functions, the Dirac equation in the space of constant torsion, Minkowski metric and straight line geodesics is considered. Solutions of the equation are given, showing the particular way in which the energy degeneracy of the states with different spin projections is removed in the presence of torsion.

scholarly journals On the Mathematical Foundations of Causal Fermion Systems in Minkowski Space

2020 ◽  
Author(s):  
Marco Oppio
Keyword(s):  
Correlation Function ◽  
Dirac Equation ◽  
Minkowski Space ◽  
Planck Scale ◽  
Solution Space ◽  
Maximal Rank ◽  
Local Correlation ◽  
Fermion Systems ◽  
Dirac Sea ◽  
Mathematical Foundations

AbstractThe emergence of the concept of a causal fermion system is revisited and further investigated for the vacuum Dirac equation in Minkowski space. After a brief recap of the Dirac equation and its solution space, in order to allow for the effects of a possibly nonstandard structure of spacetime at the Planck scale, a regularization by a smooth cutoff in momentum space is introduced, and its properties are discussed. Given an ensemble of solutions, we recall the construction of a local correlation function, which realizes spacetime in terms of operators. It is shown in various situations that the local correlation function maps spacetime points to operators of maximal rank and that it is closed and homeomorphic onto its image. It is inferred that the corresponding causal fermion systems are regular and have a smooth manifold structure. The cases considered include a Dirac sea vacuum and systems involving a finite number of particles and antiparticles.

GENERALIZED VOLKOV PROBLEM

1991 ◽  
Vol 06 (27) ◽  
pp. 4831-4841
Author(s):  
GERMAN V. SHISHKIN ◽  
MOHAMMED A. YASIN
Keyword(s):  
Dirac Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Minkowski Space ◽  
Space Time ◽  
Wave Fields ◽  
Cartesian Coordinates ◽  
First Order ◽  
Minkowski Space Time ◽  
External Wave

We consider the Dirac equation in Minkowski space-time in Cartesian coordinates with external wave fields of different tensor structures, namely in the presence of scalar, vector, pseudoscalar, pseudovector, coupled vector and tensor, and coupled vector and pseudovector waves, i.e. we consider the generalized Volkov problem. The solution of the Dirac equation is reduced to that of a system of four equations, two of which are first-order ordinary differential equations and two are algebraic ones. Series of new solutions of the Dirac equation are obtained.

Sign in / Sign up

Export Citation Format

Share Document