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arXiv · 0708.1703

Point-form quantum field theory

E. P. Biernat·W. H. Klink·W. Schweiger·S. Zelzer
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Abstract

We examine canonical quantization of relativistic field theories on the forward hyperboloid, a Lorentz-invariant surface of the form $x_μx^μ= τ^2$. 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 Poincaré 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.

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E. P. Biernat, W. H. Klink, W. Schweiger, S. Zelzer. 2007-08-13. Point-form quantum field theory. https://doi.org/10.1016/j.aop.2007.09.004

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