Classical Yang-Mills-Dirac equations: Qualitative analysis of some solutions with a noncompact symmetry group

1996 ◽  
Vol 38 (3) ◽  
pp. 237-255 ◽  
Author(s):  
J. -P. Antoine ◽  
I. Mahara
Keyword(s):  
Qualitative Analysis ◽  
Symmetry Group ◽  
Yang Mills ◽  
Dirac Equations

scholarly journals Lévy differential operators and Gauge invariant equations for Dirac and Higgs fields

2019 ◽  
Vol 22 (01) ◽  
pp. 1950001 ◽  
Author(s):  
Boris O. Volkov
Keyword(s):  
Differential Operators ◽  
Equations Of Motion ◽  
Parallel Transport ◽  
System Of Differential Equations ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Dirac Equations ◽  
Lévy Laplacian ◽  
Higgs Fields

We study the Lévy infinite-dimensional differential operators (differential operators defined by the analogy with the Lévy Laplacian) and their relationship to the Yang–Mills equations. We consider the parallel transport on the space of curves as an infinite-dimensional analogue of chiral fields and show that it is a solution to the system of differential equations if and only if the associated connection is a solution to the Yang–Mills equations. This system is an analogue of the equations of motion of chiral fields and contains the Lévy divergence. The systems of infinite-dimensional equations containing Lévy differential operators, that are equivalent to the Yang–Mills–Higgs equations and the Yang–Mills–Dirac equations (the equations of quantum chromodynamics), are obtained. The equivalence of two ways to define Lévy differential operators is shown.

Dirac equations for generalised Yang-Mills systems

1985 ◽  
Vol 162 (1-3) ◽  
pp. 143-147 ◽  
Author(s):  
O. Lechtenfeld ◽  
W. Nahm ◽  
D.H. Tchrakian
Keyword(s):  
Yang Mills ◽  
Dirac Equations

(2, 0)-SUPER-YANG–MILLS COUPLED TO NONLINEAR σ-MODELS

2001 ◽  
Vol 16 (02) ◽  
pp. 189-199
Author(s):  
M. S. GÓES-NEGRÃO ◽  
M. R. NEGRÃO ◽  
A. B. PENNA-FIRME
Keyword(s):  
Symmetry Group ◽  
Light Cone ◽  
Ordinary Matter ◽  
Yang Mills

Considering a class of (2, 0)-super-Yang–Mills multiplets that accommodate a pair of independent gauge potentials in connection with a single symmetry group, we present here their coupling to ordinary matter and to nonlinear σ-models in (2, 0)-superspace. The dynamics and the couplings of the gauge potentials are discussed and the interesting feature that comes out is a sort of "chirality" for one of the gauge potentials once light-cone coordinates are chosen.

scholarly journals SO(4) Reduction of the SU(N) Yang–Mills–Dirac equations

1986 ◽  
Vol 27 (2) ◽  
pp. 620-626 ◽  
Author(s):  
M. Légaré ◽  
J. Harnad
Keyword(s):  
Yang Mills ◽  
Dirac Equations
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