GENERALIZED HAMILTONIAN FORMALISM FOR FIELD THEORY: CONSTRAINT SYSTEMS

In the framework of the geometric formulation of field theory,classical fields are represented by sections of fibred manifolds, andtheir dynamics is phrased in jet manifold terms. The Hamiltonianformalism in fibred manifolds is the multisymplectic generalization ofthe Hamiltonian formalism in mechanics when canonical momentacorrespond to derivatives of fields with respect to all worldcoordinates, not only to time. This book is devoted to the applicationof this formalism to fundamental field models including gauge theory,gravitation theory, and spontaneous symmetry breaking. All thesemodels are constraint ones. Their Euler-Lagrange equations areunderdetermined and need additional conditions. In the Hamiltonianformalism, these conditions appear automatically as a part of theHamilton equations, corresponding to different Hamiltonian formsassociated with a degenerate Lagrangian density. The general procedurefor describing constraint systems with quadratic and affine Lagrangiandensities is presented.