Abstract
We comment on canonical quantization of relativistic field theories on a Lorentz-invariant surface of the form x 2 = τ2. By this choice of the quantization surface all components of the four-momentum operator become interaction dependent, whereas the generators of Lorentz transformations stay free of interactions – a feature characteristic for Dirac’s “point-form” of relativistic dynamics. In the sequel we demonstrate how field theoretical concepts may enter the framework of relativistic quantum mechanics. To this aim we employ a Poincaré-invariant approximation scheme, which allows to reduce a field theoretical many-body problem to a multichannel problem for a Bakamjian-Thomas-type mass operator. As an application of this multichannel formalism we will discuss the scattering of an electron by a (confined) quark-antiquark pair. It will be sketched how an electromagnetic meson form factor can be extracted from the one-photon exchange optical potential.
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Correspondence: W. Schweiger, Institut für Physik, Universität Graz, Universitätsplatz 5, 8010 Graz, Austria
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Biernat, E., Fuchsberger, K., Klink, W. et al. Point-form quantum field theory and meson form factors. Few-Body Syst 44, 311–314 (2008). https://doi.org/10.1007/s00601-008-0316-5
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DOI: https://doi.org/10.1007/s00601-008-0316-5