Relativistic Hamiltonian Dynamics for Three-Body Systems
Dr. Willibald Plessas
Abstract: After a short introduction to the cornerstones of Poincare-invariant quantum mechanics I shall address the problem of the description of baryons as relativistic systems of three constituent quarks. It amounts to solving the relativistic constituent-quark model (RCQM) via an invariant mass operator incorporating the dynamics of low-energy quantum chromodynamics (QCD).
By the end of the 1990's we had developed a RCQM with the quark-quark dynamics based on confinement and Goldstone-boson exchange (GBE). We succeeded to solve it with high accuracy for baryon ground and excited states both in momentum space (via Faddeev integral equations) and in configuration space (via a stochastic variational method). In this way we had achieved a unified description of the spectroscopy of all baryons with up, down, and strange flavor content [1]. The next challenge was to describe also the structure of baryons as seen by probes under electromagnetic, weak, and gravitational interactions, i.e. calculating covariant form factors from matrix elements of the corresponding current operators between baryon eigenstates. Evidently this should have been done in accordance with the full Poincare algebra observing above all Lorentz invariance.
We in Graz were lucky, as it was the time when Bill Klink had arrived in Graz and essentially told us, how to apply the point form of relativistic dynamics to produce covariant results for electroweak nucleon form factors [2,3]. A series of papers with results along the same line followed in the years thereafter. I shall discuss some key results showing that Poincare invariance is mandatory for calculating baryon properties. Thereby it will also become clear that the point form offers advantages over the instant and front forms, especially when applying the current operators in the spectator approximation [4].
[1] L.Ya. Glozman, W.Plessas, K. Varga, and R.F. Wagenbrunn: Unified description of light and strange baryon spectra. Phys. Rev. D 58 (1998) 094030
[2] R.F. Wagenbrunn, S. Boffi, W. Klink, W. Plessas, and M. Radici: Covariant electromagnetic nucleon form factors from the Goldstone-boson-exchange quark model. Phys. Lett. B 511 (2001) 33
[3] L.Ya. Glozman, M. Radici, R.F. Wagenbrunn, S. Boffi, W. Klink, and W. Plessas: Covariant axial form factor of the nucleon in a chiral constituent quark model. Phys. Lett. B 516 (2001) 183
[4] W. Plessas: The constituent quark model - Nowadays. Int. J. Mod. Phys. A 30 (2015) 1530013
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