%0 Journal Article
%T Point-form quantum field theory
%A E. P. Biernat
%A W. H. Klink
%A W. Schweiger
%A S. Zelzer
%J Physics
%D 2007
%I arXiv
%R 10.1016/j.aop.2007.09.004
%X 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 affected by interactions (if present), whereas rotation and boost generators remain interaction free -- a feature characteristic of Dirac's `` point-form\rq\rq 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 Poincar\'e 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.
%U http://arxiv.org/abs/0708.1703v1