Matter-coupled Yang-Mills system in Minkowski space. II. Invariant solutions in the presence of Dirac spinor fields
(1982) Physical review. D, Particles and fields — Vol. 25, n° 2, p. 484-501 (1982)
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- For pt.I see ibid., vol.24, no.12, p.3179-83 (1981). 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 invariance of the Lagrangian, the solutions are obtained by considering the system over the compactification /b M/ macr of Minkowski space. /b M/ macr is diffeomorphic to SU(2) otimes U(1)~/b S//sup 3/*/b S//sup 1/ and the action of the conformal group upon it is identified with that of SU(2,2) on SU(2) otimes U(1). The equations are simplified by using as Ansatze gauge and Dirac fields that are both invariant under the following (for combinations of the following) subtractions of SU(2,2): (i) left SU(2)/sub L/ translations, (ii) right SU(2)/sub R/ translations, (iii) left action of SU(2)/sub L/ otimes SU(2)/sub R /, and (iv) U(1) translations. All (real and complex) SU(2)/sub L / otimes U(1)-invariant solutions are obtained. The pullback of these solutions to Minkowski space leads to regular configurations with finite energy.
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Doneux, J., & Saint-Aubin, Y. (1982). Matter-coupled Yang-Mills system in Minkowski space. II. Invariant solutions in the presence of Dirac spinor fields. Physical review. D, Particles and fields, 25(2), 484-501. https://hdl.handle.net/2078.5/86269 (Original work published 1982)