Theory of strings

The theory of strings is briefly introduced. The string as a physical object can appear in several different contents in particle physics. Among the various physical manifestations of strings, the possible role of large scale strings in cosmology is discussed. The strings relevant to this problem are superheavy ones in non-Abelian gauge theories in the Higgs phase. First of all, mathematical description is presented. Formulating a Hamilton-Jacobi theory for string system may serve as a first step toward quantization. A family of minimal surfaces can be described in terms of a vector field, which is an Abelian gauge field with special properties. Two examples of formulations are given. The merit of this formulation lies in the fact that the QCD Lagrangian may be converted into an effective Abelian Lagrangian. The theory starts from an SU(n) Lagrangian. The action over non-Abelian variables is integrated, fixing all the Abelian field. The results will be an effective action for the Abelian fields. It should be in general non-local and nonlinear. Test of formalism is done in two dimensions. (Kato, T.)