Letters m Mathematical Physics 22:203 210, 1991. c,t~ 1991 Kluwer Academic Publishers. Printed in the Netherlands. 203 A Monopole-Like Classical Solution to a Purely Fermionic Model of Even Dimensions D. DIBEKCI Kocaeli Campus, Yildiz University, lzmit, Turkey M. HORTACSU, J. KALAYCI, and H. OZBEK Physics Department, FaculO, of Science and Letters, lstanbul Technical Unwersity, Maslak, lstanbul 80626, Turkey (Received. 21 February 1991) Abstract. We present a static solutmn to the classical field equations of a purely spinorial model with SO(2n) internal symmetry in 2n dimensions. The model contains composite vector fields which have solutions of the Wu-Yang monopole type. AMS subject classifications (1991). 81T13, 81T40. Magnetic monopoles have received a great deal of attention during the last nearly 60 years, ever since Dirac laid down the theoretical foundations for them [l]. In the non-Abelian pure gauge theories which are classically conformally invariant, whole sets of monopole solutions have been found. The first solution is the Wu-Yang monopole [2]. Later, finite energy single monopole solutions were found [3] and finite energy multi-monopole solutions were found some l0 years later [4]. Nahm applied the Atiyah-Drinfeld-Hitchin-Manin method [5] to the construction of multi-monopoles [6]. When alternative models for pure gauge theories in even higher dimensions were suggested by several authors [7], it was a logical step to search for such solutions in these theories. In a previous paper [8], we showed that monopole solutions did indeed exist in six dimensions. The most interesting set of these solutions read A, = 0. (la) x, (lb) A, = -- ia,i 2r 2 . These solutions give nonvanishing field tensor, F,,v. Another development is the study of purely fermionic models where vector particles appear as composites. These models are generalizations of the conformally invariant Thirring model [9] in higher dimensions, with the hope of making Heisenberg's dream [ 10] come true by describing the world only by spinors. Gursey proposed such a model which was conformally invariant in four dimensions with noninteger powers of the field [11]. Kortel found classical solutions to this model