l’bag” (“bubble” or llshell’*) by the strong interaction of an elementary fermion quark field with a quartically self-coupled neutral scalar field. The L%AC bag is derived using a variational approach and a semi-classical (“tree approxima-

These lectures describe some efforts to understand quark confinement in the context of quantum field theory. First we describe the formation of the SLAC l’bag” (“bubble” or llshell’*) by the strong interaction of an elementary fermion quark field with a quartically self-coupled neutral scalar field. The L%AC bag is derived using a variational approach and a semi-classical (“tree approximation”) treatment of the field theory. Physical properties of the SLAC bag are discussed. Next we show that the SLAC bag is “soft” to deformations and discuss the general formalism for studying bag deformations and the low lying bag excitations developed by R . Giles. Next we discuss the relation of the SLAC to the MIT bag. Finally we discuss the quantum corrections to the semi-classical treatment of field theory used in constructing the SLAC bag. Beyond the oneloop approximation we describe the initial progress in formulating the field theory on a discrete lattice and studying its quantum behavior and spontaneous symmetry breaking using variational methods. (Lectures given at the “Ettore Majorana Int’l Summer School,” Erice, Sicily, 11 July 1 August 1975.) *Work supported by the U. S. Energy Research and Development Administration.