The theory of overdetermined linear systems and its applications to non-linear field equations

1984 ◽  
Vol 1 (2) ◽  
pp. 139-172 ◽  
Author(s):  
Michel Dubois-Violette
Keyword(s):  
Linear Systems ◽  
Field Equations ◽  
Overdetermined Linear Systems ◽  
Non Linear ◽  
Linear Field

Non-Linear Generalization of the Relativistic Schrödinger Equations

1996 ◽  
Vol 51 (9) ◽  
pp. 965-982
Author(s):  
U. Ochs ◽  
M. Sorg
Keyword(s):  
Numerical Results ◽  
Schrodinger Equations ◽  
Higgs Potential ◽  
Schrödinger Equations ◽  
Field Equations ◽  
Non Linear ◽  
Klein Gordon ◽  
The Universe ◽  
Linear Field

Abstract The theory of the Relativistic Schrödinger Equations is further developped and extended to non-linear field equations. The technical advantage of the Relativistic Schrödinger approach is demonstrated explicitly by solving the coupled Einstein-Klein-Gordon equations including a non-linear Higgs potential in case of a Robertson-Walker universe. The numerical results yield the effect of dynamical self-diagonalization of the Hamiltonian which corresponds to a kind of quantum de-coherence being enabled by the inflation of the universe.

On a linearization program of non-linear field equations

1980 ◽  
Vol 94 (4) ◽  
pp. 518-522 ◽  
Author(s):  
M. Flato ◽  
J. Simon
Keyword(s):  
Field Equations ◽  
Non Linear ◽  
Linear Field

Particle states of a quantized meson field

1961 ◽  
Vol 262 (1309) ◽  
pp. 237-245 ◽  
Keyword(s):  
Field Theory ◽  
Classical Field Theory ◽  
Classical Field ◽  
Quantum States ◽  
Meson Field ◽  
Field Equations ◽  
Non Linear ◽  
Linear Field

A simple non-linear field theory is considered as the model for a recently proposed classical field theory of mesons and their particle sources. Quantization may be made according to canonical procedures; the problem is to show the existence of quantum states corresponding with the particle-like solutions of the classical field equations. A plausible way to do this is suggested.

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