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How can we relate the constraint structure and constraint dynamics of thegeneral gauge theory in the Hamiltonian formulation with specific features ofthe theory in the Lagrangian formulation, especially relate the constraintstructure with the gauge transformation structure of the Lagrangian action? Howcan we construct the general expression for the gauge charge if the constraintstructure in the Hamiltonian formulation is known? Whether can we identify thephysical functions defined as commuting with first-class constraints in theHamiltonian formulation and the physical functions defined as gauge invariantfunctions in the Lagrangian formulation? The aim of the present article is toconsider the general quadratic gauge theory and to answer the above questionsfor such a theory in terms of strict assertions. To fulfill such a program, wedemonstrate the existence of the so-called superspecial phase-space variablesin terms of which the quadratic Hamiltonian action takes a simple canonicalform. On the basis of such a representation, we analyze a functionalarbitrariness in the solutions of the equations of motion of the quadraticgauge theory and derive the general structure of symmetries by analyzing asymmetry equation. We then use these results to identify the two definitions ofphysical functions and thus prove the Dirac conjecture.Comment: LaTex file, 18 page

General quadratic gauge theory: constraint structure, symmetries and physical functions