Point-form quantum field theory

Abstract

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 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.

30 pages

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Cited by in corpus (7)

• Point-Form Hamiltonian Dynamics and Applications
• Electromagnetic meson form factor from a relativistic coupled-channel approach
• Point-form quantum field theory
• Lorentz-boost eigenmodes
• Electromagnetic Properties of Few-Body Systems Within a Point-Form Approach
• Point-form dynamics of quasistable states
• Point-form quantum field theory and meson form factors