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

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.

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

CLASSICAL YANG-MILLS-DIRAC SYSTEM WITH CONFORMAL SYMMETRY: A GEOMETRICAL ANALYSIS

1994 ◽  
Vol 09 (37) ◽  
pp. 3431-3444 ◽  
Author(s):  
J.-P. ANTOINE ◽  
L. DABROWSKI ◽  
I. MAHARA
Keyword(s):  
Minkowski Space ◽  
Gauge Group ◽  
Gauge Transformation ◽  
Conformal Symmetry ◽  
Conformal Group ◽  
Dirac System ◽  
Geometrical Analysis ◽  
Yang Mills ◽  
Dirac Equations

We consider classical Yang-Mills-Dirac equations on Minkowski space, with gauge group SU(2), and look for solutions invariant (up to a gauge transformation) under a four-dimensional subgroup of the conformal group. In each of the four different cases that we analyze, the equations admit non-Abelian solutions, but these cannot be obtained analytically. In addition, some cases admit solutions with chiral spinors that may be physically relevant. All these solutions are singular.

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