Generalized canonical formalism and S-matrix of a theory with constraints of a general form

A method for the canonical quantization of systems with first-class and second-class constraints of arbitrary rank is developed. The effectiveness of the method is demonstrated for the examples of Yang-Mills and gravitational fields. Generalized quantization is carried out and an S-matrix in configuration space is obtained for theories of relativistic membranes having the form of the generalization of string theories to the case of an expanded spatial realization. It is shown that the theory of membranes in n = 1 measurement space is a system with constraints of rank n.