Hamiltonians without Parametrization

Abstract

Theories which are covariant with respect to transformation groups involving arbitrary functions cannot be of the Cauchy-Kowalewski type. Therefore, it would appear that such theories cannot be cast into a hamiltonian formalism. However, a hamiltonian function can be formed although it is, to a certain extent, arbitrary. This lack of uniqueness is an immediate consequence of the covariance requirements. The adoption of a particular hamiltonian function destroys the covariance of the theory. This situation is similar to the introduction of "cordinate conditions" in the theory of gravitation or the use of the Lorentz gauge condition in electrodynamics.