Relation between instant and light-front formulations of quantum field theory

The scattering equivalence of quantum field theories formulated with light-front and instant-form kinematic subgroups is established using nonperturbative methods. The difficulty with field theoretic formulations of Dirac's forms of dynamics is that the free and interacting unitary representations of the Poincare group are defined on inequivalent representations of the Hilbert space, which means that the concept of kinematic transformations must be modified on the Hilbert space of the field theory. This work addresses this problem by assuming the existence of a field theory with the expected properties and constructs equivalent representations with instant and front-form kinematic subgroups. The underlying field theory is not initially associated with an instant form or light-front form of the dynamics. In this construction the existence of a vacuum and one-particle mass eigenstates is assumed and both the light-front and instant-form representations are constructed to share the same vacuum and one-particle states. If there is spontaneous symmetry breaking there will be a 0 mass particle in the mass spectrum (assuming no Higgs mechanism). The free field Fock space plays no role. There is no "quantization" of a classical theory. The property that survives from the perturbative approach is the notion of a kinematic subgroup, which means kinematic Poincar ' e transformations can be trivially implemented by acting on suitable basis vectors. This nonperturbative approach avoids dealing with issues that arise in perturbative treatments where is it necessary to have a consistent treatment of renormalization, rotational covariance, and the structure of the light-front vacuum. While addressing these issues in a computational framework is the most important unanswered question for applications, this work may provide some insight into the nature of the expected resolution and identifies the origin of some of differences between the perturbative and nonperturbative approaches.