scholarly journals Darboux transformations for a generalized Dirac equation in two dimensions

2010 ◽  
Vol 51 (11) ◽  
pp. 113501 ◽  
Author(s):  
Ekaterina Pozdeeva ◽  
Axel Schulze-Halberg
Keyword(s):  
Dirac Equation ◽  
Two Dimensions ◽  
Darboux Transformations ◽  
Generalized Dirac Equation

scholarly journals Higher-order Darboux transformations for two-dimensional Dirac systems with diagonal matrix potential

2021 ◽  
Vol 2090 (1) ◽  
pp. 012038
Author(s):  
A Schulze-Halberg
Keyword(s):  
Dirac Equation ◽  
Explicit Form ◽  
Higher Order ◽  
Diagonal Matrix ◽  
Two Dimensional ◽  
Darboux Transformations ◽  
Dirac Systems ◽  
Matrix Potential ◽  
De Vries ◽  
The Matrix

Abstract We construct the explicit form of higher-order Darboux transformations for the two-dimensional Dirac equation with diagonal matrix potential. The matrix potential entries can depend arbitrarily on the two variables. Our construction is based on results for coupled Korteweg-de Vries equations [27].

scholarly journals Nonstandard Dirac equations for nonstandard spinors

2014 ◽  
Vol 23 (14) ◽  
pp. 1444007 ◽  
Author(s):  
A. G. Nikitin
Keyword(s):  
Dirac Equation ◽  
Mass Term ◽  
Charge Conjugation ◽  
Poincaré Group ◽  
Poincare Group ◽  
Dirac Equations ◽  
Generalized Dirac Equation ◽  
Carrier Space ◽  
New Look

Generalized Dirac equation with operator mass term is presented. Its solutions are nonstandard spinors (NSS) which, like eigenspinoren des Ladungskonjugationsoperators (ELKO), are eigenvectors of the charge conjugation and dual-helicity operators. It is demonstrated that in spite of their noncovariant nature the NSS can serve as a carrier space of a representation of Poincaré group. However, the corresponding boost generators are not manifestly covariant and generate nonlocal momentum dependent transformations, which are presented explicitly. These results can present a new look on group-theoretical grounds of ELKO theories.

WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE CHERN–SIMONS–DIRAC SYSTEM IN TWO DIMENSIONS

2013 ◽  
Vol 10 (04) ◽  
pp. 735-771 ◽  
Author(s):  
MAMORU OKAMOTO
Keyword(s):  
Cauchy Problem ◽  
Dirac Equation ◽  
Sobolev Space ◽  
Gauge Invariance ◽  
Two Dimensions ◽  
Well Posedness ◽  
Dirac System ◽  
The Cauchy Problem ◽  
Chern Simons ◽  
Well Posed

We consider the Cauchy problem associated with the Chern–Simons–Dirac system in ℝ1+2. Using gauge invariance, we reduce the Chern–Simons–Dirac system to a Dirac equation and we uncover the null structure of this Dirac equation. Next, relying on null structure estimates, we establish that the Cauchy problem associated with this Dirac equation is locally-in-time well-posed in the Sobolev space Hs for all s > 1/4. Our proof uses modified L4-type estimates.

scholarly journals Bending and flexural phonon scattering: Generalized Dirac equation for an electron moving in curved graphene

2012 ◽  
Vol 407 (12) ◽  
pp. 2002-2008 ◽  
Author(s):  
Richard Kerner ◽  
Gerardo G. Naumis ◽  
Wilfrido A. Gómez-Arias
Keyword(s):  
Dirac Equation ◽  
Phonon Scattering ◽  
Generalized Dirac Equation
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