We consider a general quadratic gauge theory. Our aim is to prove for such a theory a set of generic properties which usually are supposed to be valid for gauge theories. To fulfill such a program, we demonstrate the existence of the so-called superspecial phase-space variables, in which the quadratic Hamiltonian action of the gauge theory takes a simple canonical form. On the basis of such a representation, we analyze the functional arbitrariness in solutions of equations of motion and derive a general structure of symmetries by analyzing a symmetry equation. In particular, we establish the relation between the constraint structure of the theory and the structure of its gauge transformations, we prove the famous Dirac conjecture, and identify the definition of a physical function as that which commutes with first-class constraints with the alternative one, as that which is gauge invariant on the extremals.
展开▼
