In this paper we study the large $N_c$ limit of SO(N_c) gauge theory coupled to a real scalar field following ideas of Rajeev. We see that the phase space of this resulting classical theory is Sp_1(H)/U(H_+) which is the analog of the Siegel disc in infinite dimensions. The linearized equations of motion give us a version of the well-known 't Hooft equation of two dimensional QCD.Comment: 16 pages, no figure

In this paper we study the large N c limit of SO(N c ) gauge theory coupled to a Majorana field and a real scalar field in 1ϩ1 dimensions extending ideas of Rajeev ͓Int. J. Mod. Phys. A 9, 5583 ͑1994͔͒. We show that the phase space of the resulting classical theory of bilinears, which are the mesonic operators of this theory, iswhere H͉H refers to the underlying complex graded space of combined one-particle states of fermions and bosons and H ϩ ͉H ϩ corresponds to the positive frequency subspace. In the begining to simplify our presentation we discuss in detail the case with Majorana fermions only ͓the purely bosonic case is treated in Toprak and Turgut, J. Math. Phys. 43, 1340 ͑2002͔͒. In the Majorana fermion case the phase space is given by O 1 (H)/U(H ϩ ), where H refers to the complex one-particle states and H ϩ to its positive frequency subspace. The meson spectrum in the linear approximation again obeys a variant of the 't Hooft equation. The linear approximation to the boson/fermion coupled case brings an additonal bound state equation for mesons, which consists of one fermion and one boson, again of the same form as the well-known 't Hooft equation.