A new picture for light front dynamics

A new picture for light front dynamics is developed which employs an arbitrary, external, lightlike four-vector ξ. The state vectors and operators in this so-called ξ-picture are related to the state vectors and operators in the standard formulation of light front dynamics by a unitary transformation which depends on the unit vector u = -ξ |ξ|, where ξ is the three-vector part of ξ. This unitary transforation is somewhat analogous to the transformation which relates the Heisenberg picture to the interaction picture, with the two angles that specify the direction of u playing the role of the time. Just as the interaction picture is designed to cope with the interaction in the Hamiltonian, the ξ-picture is designed to cope with the interaction in the angular momentum operator J. In the ξ-picture the action of the angular momentum operator is equivalent to the action of S(u) = J₀ + L(u), where J₀ is the noninteracting part of J and L(u) is an orbital angular momentum operator. The standard theory of angular momentum can be used to construct eigenstates of S² and S₃; however, some of these states are spurious. The physical states can be obtained by imposing a dynamical constraint equation. A momentum space representation for the ξ-picture state vectors and operators is developed. It is shown that the wavefunctions for states of well-defined total four-momentum factor into an invariant δ-function and a function which depends on relative three-momentum variables q_i and a unit vector n, which is u in a cm frame. Under a Lorentz transformation, the transformation of a state vector is equivalent to a three-rotation of the q_i's and n. The general formalism is applied to a model which describes a two-particle system for which there exists manifestly covariant wavefunctions of the space-time variables for the two particles. The covariant wavefunctions satisfy the standard constraint of covariant constraint dynamics.