Global solutions to non linear Dirac equations in Minkowski space

2006 ◽  
pp. 1-11 ◽  
Author(s):  
Alain Bachelot
Keyword(s):  
Minkowski Space ◽  
Global Solutions ◽  
Dirac Equations ◽  
Non Linear

scholarly journals Some global solutions of the Yang-Mills equations in Minkowski space

1981 ◽  
Vol 81 (2) ◽  
pp. 171-187 ◽  
Author(s):  
Robert T. Glassey ◽  
Walter A. Strauss
Keyword(s):  
Minkowski Space ◽  
Global Solutions ◽  
Yang Mills

On the twistor description of massive fields

1981 ◽  
Vol 374 (1758) ◽  
pp. 431-445 ◽  
Keyword(s):  
Minkowski Space ◽  
Complex Manifold ◽  
Twistor Space ◽  
Spin Operator ◽  
Dirac Equations ◽  
Penrose Transform ◽  
Twistor Description ◽  
Integral Formulae ◽  
Massless Fields ◽  
Massive Fields

This paper forms a part of the twistor programme whereby constructions of physics on Minkowski space are transferred, it is hoped, to simpler constructions on Penrose’s twistor-space . We show how the Penrose transform may be used to describe solutions of the Dirac equations on Minkowski space in terms of certain cohomology classes on a related five-dimensional complex manifold. This is accomplished along the same lines as the corresponding representation of massless fields. It means that Penrose’s integral formulae for massive fields may be interpreted cohomologically. We also give a brief discussion of the spin operator in twistor space.

Equations de Schrödinger non linéaires en dimension deux

1979 ◽  
Vol 84 (3-4) ◽  
pp. 327-346 ◽  
Author(s):  
Thierry Cazenave
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Asymptotic Behaviour ◽  
Blow Up ◽  
Global Solutions ◽  
Two Dimensions ◽  
Linear Optics ◽  
Non Linear Optics ◽  
Non Linear ◽  
The Cauchy Problem

SynopsisThis paper is devoted to the study of some non linear Schrödinger equations in two dimensions, arising in non linear optics; in particular, it is concerned with solutions to the Cauchy problem. The problem of global existence and regularity of the solutions, the asymptotic behaviour of global solutions, and the blow-up of non global solutions are studied.

scholarly journals On global solutions of the Maxwell-Dirac equations

1987 ◽  
Vol 112 (1) ◽  
pp. 21-49 ◽  
Author(s):  
M. Flato ◽  
Jacques Simon ◽  
Erik Taflin
Keyword(s):  
Global Solutions ◽  
Dirac Equations
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