Singular Lagrangian and the Dirac-Faddeev Method: Existence Theorem of Constraints in 'Standard Form'

Abstract

Rigorous basis is given to the Dirac-Faddeev method, i.e., the Feynman integral with constraints (1st-class and/or 2nd-class), by proving existence theorem of constraints in ‘standard form’ for the restricted submanifold of definite dimension. The theorem states that such canonical variables exist for a given restricted submanifold that the submanifold is specified by putting those canonical variables equal to zero. This theorem will also give straightforward understanding of concepts in the Dirac formalism, e.g., Dirac bracket.