A gauge-independent canonical formalism for the Dirac-Maxwell theory (Q1077057)

The canonical structure of particle mechanics as well as classical field theory is determined by the symplectic geometry of the cotangent bundle of the configuration manifold. The author describes the canonical structure of the space of Cauchy data for the classical Dirac-Maxwell field (spin s\(=\), the charge \(e=\pm 1\) and the mass m particle interacting with the electromagnetic field). The field equation of the theory can be obtained from the standard Dirac Lagrangian. For a large class of Cauchy data (called regular bispinors) the author finds an effective gauge-independent parametrization of the states of the field. As the canonical structure of the Dirac field theory corresponds to the canonical structure of the cotangent bundle, regular bispinors on a Cauchy surface are described by elements of the bundle cotangent to the manifold of all the orthonormal triads on the Cauchy surface.