Hamiltonian dynamics of fields in front form

Abstract

We propose a new approach for constructing the Hamiltonian dynamics for a coupled Dirac field Ψ( x), quantized on the light-front t+ z = 0, in which the momentum representation of fields is used to obtain the anti-commutator for Ψ( x) and its momentum conjugate π( x). Aside from the usual definition of π( x), the Hamiltonian, the anti-commutators and the Hamiltonian equations of motion, we need a subsidiary condition for Ψ( x) to make the front-form dynamics consistent and valid in any inertial frame. By treating all components of Ψ( x) in the same manner and retaining the subsidiary condition, we make the theory simple and elegant. In contrast to the infinite-momentum-frame approach, there is no non-covariant term in the Hamiltonian and the propagator in our approach. The resultant Feynman rules make the equivalence of the scattering matrices between the front-form dynamics and the conventional dynamics become apparent. The difference between the two forms of dynamics is also discussed.