Introduction of True Variables and Consistency of Hamiltonian Formalism

In the presence of constraints true variables in the classical theory of non-linear field are defined in a consistent way, both internally and externally. When the constraints are of the second class, they are formed from the original variables by adding a linear combination of the constraints in such a way that they have vanishing Poisson brackets with the constraints. If there are the first class constraints these are first converted into the second class with the aid of auxiliary conditions which play the role of fixing gauges. As a straightforward application the true variables for Yang-Mills field are formed. Perhaps it will be right to say that when the first class constraints exist we cannot have an image of particle without accompanied by its potential field; true variables take this into account. The internal and external consistencies of canonical formalism for the gravitational field employed by Arnowitt-Deser-Misner and Dirac are discussed and the non-vanishing Hamiltonian of the gravitational field is obtained unambiguously. Finally Burton-Touschek's question about the commutation relation derived from Schwinger's dynamical principle is discussed from the standpoint of our procedure and a new method of deriving the correct commutation relation from the Feynman amplitude is given.