Matter-coupled Yang-Mills system in Minkowski space. II. Invariant solutions in the presence of Dirac spinor fields
Classical solutions to the Minkowskian field equations of a Yang-Mills system coupled to an isospinor of massless Dirac fields are found. The Dirac fields are taken in the fundamental representation of SU(2). In view of the conformal and Weyl inveriance of the Lagrangian, the solutions are obtained by considering the system over the compactification M-bar of Minkowski space. M-bar is diffeomorphic to SU(2)xU(1)approx.S/sup 3/ x S/sup 1/ and the action of the conformal group upon it is identified with that of SU(2,2) on SU(2)xU(1). The equations are simplified by using as Ansatze gauge and Dirac fields that are both invariant under the following (or combinations of the following) subactions of SU(2,2): (i) left SU(2)/sub L/ translations, (ii) right SU(2)/sub R/ translations, (iii) the left action of SU(2)/sub L/xSU(2)/sub R/, and (iv) U(1) translations. All (real and complex) SU(2)/sub L/xU(1)/sub R/xU(1)-invariant solutions are obtained. The pullback of these solutions to Minkowski space leads to regular configurations with finite energy.
- Research Organization:
- Institut de Physique Theorique, Universite Catholique de Louvain, 1348 Louvian-la-Neuve, Belgium
- DOE Contract Number:
- DE-AC02-76ER03069
- OSTI ID:
- 5622920
- Journal Information:
- Phys. Rev. D; (United States), Vol. 25:2
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
YANG-MILLS THEORY
FIELD EQUATIONS
CONFORMAL INVARIANCE
DIRAC EQUATION
MINKOWSKI SPACE
SPACE-TIME
SPINORS
SU-2 GROUPS
U-1 GROUPS
DIFFERENTIAL EQUATIONS
EQUATIONS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
SPACE
SU GROUPS
SYMMETRY GROUPS
U GROUPS
WAVE EQUATIONS
645400* - High Energy Physics- Field Theory