We shortly review point-form quantum field theory, i.e. the canonical quantization of a relativistic field theory on a Lorentz-invariant surface of the form $x_mu x^mu = tau^2$. As an example of how point-form quantum field theory may enter the frame
work of relativistic quantum mechanics we discuss the calculation of the electromagnetic form factor of a confined quark-antiquark pair (e.g. the pion).
We examine canonical quantization of relativistic field theories on the forward hyperboloid, a Lorentz-invariant surface of the form $x_mu x^mu = tau^2$. This choice of quantization surface implies that all components of the 4-momentum operator are a
ffected by interactions (if present), whereas rotation and boost generators remain interaction free -- a feature characteristic of Diracs `` point-formrqrq of relativistic dynamics. Unlike previous attempts to quantize fields on space-time hyperboloids, we keep the usual plane-wave expansion of the field operators and consider evolution of the system generated by the 4-momentum operator. We verify that the Fock-space representations of the Poincare generators for free scalar and spin-1/2 fields look the same as for equal-time quantization. Scattering is formulated for interacting fields in a covariant interaction picture and it is shown that the familiar perturbative expansion of the S-operator is recovered by our approach. An appendix analyzes special distributions, integrals over the forward hyperboloid, that are used repeatedly in the paper.
