Our interest is in the truncation of the infinite hierarchy of DS equations in such a way that general properties of the exact theory, such as the Ward identities and renormalizability, are not destroyed by the approximations. Methods of nonlinear functional analysis, in particular bifurcation theory, are then applied to obtain information about the nonperturbative solutions and to compute them numerically. Mathematical Properties of String Theory Elementary particle physics aims to give a consistent description of the elementary particles and their interactions. The gravitational force is described by Einstein's general relativity. The standard model is a quantum theory of elementary particles, general relativity is a classical theory.
String theory is a proposal to unify gravitation with the other forces in a single quantum theory.
In string theory it is assumed that particles manifest themselves as the different vibration modes of a stringlike structure. String theory is still in a premature stage. Although many interesting results have been obtained much work remains to be done to achieve the unification mentioned above. The investigation of string theory has led to many unexpected connections with other parts of theoretical physics and mathematics. Our particular interests are the symmetry properties of string theory, and the connections between string theory and the usual description of elementary particles in terms of pointlike objects.