Covariant Hamiltonian formalisms for particles and antiparticles

Abstract

The hyperplane and proper time formalisms are discussed mainly for the spin-half particles in the quantum case. A connection between these covariant Hamiltonian formalisms is established. It is showed that choosing the space-like hyperplanes instantaneously orthogonal to the direction of motion of the particle the proper time formalism is retrieved on the mass shell. As a consequence, the relation between the Stückelberg-Feynman picture and the standard canonical picture of quantum field theory is clarified.

19 pages, Latex, to be published in Int. J. Theor. Phys