Constraint field systems in multimomentum canonical variables

Abstract

To describe constraint field models, we apply the multimomentum Hamiltonian formalism where momenta correspond to derivatives of fields with respect to all world coordinates, not only time. If a Lagrangian density is degenerate, the Euler–Lagrange equations are underdetermined and need additional gauge-type conditions which remain elusive in general. One gets these conditions automatically as a part of the Hamilton equations, but must consider a family of Hamiltonian forms associated with the same Lagrangian density in order to exhaust solutions of the Euler–Lagrange equations. The case of degenerate quadratic and affine Lagrangian densities is elaborated. As a result, we get the universal procedure of describing constraint field systems.