A GENERAL COVARIANT SYMPLECTIC STRUCTURE FOR GRAVITATIONAL, ELECTROMAGNETIC AND DIRAC FIELDS

Abstract

We derive a general covariant symplectic structure which leads to holonomic and anholonomic formulations of Hamilton equations of motion related to the hydrodynamic picture of mechanics. Such a structure can be achieved starting from generic bilinear Hamiltonians, constructed by covariant vector, bivector or tensor fields. This feature is gage-free and it realizes a deep link toward canonical quantization for interactions like electromagnetism, gravity and Dirac fields.