Abstract
This short review summarizes recent developments and results in connection with point-form dynamics of relativistic quantum systems. We discuss a Poincaré invariant multichannel formalism which describes particle production and annihilation via vertex interactions that are derived from field theoretical interaction densities. We sketch how this rather general formalism can be used to derive electromagnetic form factors of confined quark–antiquark systems. As a further application it is explained how the chiral constituent quark model leads to hadronic states that can be considered as bare hadrons dressed by meson loops. Within this approach hadron resonances acquire a finite (non-perturbative) decay width. We will also discuss the point-form dynamics of quantum fields. After recalling basic facts of the free-field case we will address some quantum field theoretical problems for which canonical quantization on a space–time hyperboloid could be advantageous.
Similar content being viewed by others
References
Dirac P.A.M.: Forms of relativistic dynamics. Rev. Mod. Phys. 21, 392 (1949)
Biernat E.P., Klink W.H., Schweiger W., Zelzer S.: Point-form quantum field theory. Ann. Phys. 323, 1361 (2008)
Bakamjian B., Thomas L.H.: Relativistic particle dynamics, II. Phys. Rev. 92, 1300 (1953)
Keister B.D., Polyzou W.N.: Relativistic Hamiltonian dynamics in nuclear and particle physics. Adv. Nucl. Phys. 20, 225 (1991)
Foldy L.L.: Relativistic particle systems with interactions. Phys. Rev. 122, 275 (1961)
Klink W.H.: Relativistic simultaneously coupled multiparticle states. Phys. Rev. C 58, 3617 (1998)
Klink W.H.: Constructing point form mass operators from vertex interactions. Nucl. Phys. A 716, 123 (2003)
Girlanda L., Viviani M., Klink W.H.: Bakamjian–Thomas mass operator for the few-nucleon system from chiral dynamics. Phys. Rev. C 76, 044002 (2007)
Biernat E.P., Schweiger W., Fuchsberger K., Klink W.H.: Electromagnetic meson form factor from a relativistic coupled-channel approach. Phys. Rev. C 79, 055203 (2009)
Siegert A.J.F.: Note on the interaction between nuclei and electromagnetic radiation. Phys. Rev. 52, 787 (1937)
Lev F.M.: Exact construction of the electromagnetic current operator for rRelativistic composite systems. Ann. Phys. 237, 355 (1995)
Klink W.H.: Point form relativistic quantum mechanics and electromagnetic form factors. Phys. Rev. C 58, 3587 (1998)
Carbonell J., Desplanques B., Karmanov V.A., Mathiot J.F.: Explicitly covariant light-front dynamics and relativistic few-body systems. Phys. Rep. 300, 215 (1998)
Melde T., Plessas W., Sengl B.: Covariant calculation of nonstrange decays of strange baryon resonances. Phys. Rev. C 76, 025204 (2007)
Sengl B., Melde T., Plessas W.: Covariant calculation of strange decays of baryon resonances. Phys. Rev. D 76, 054008 (2007)
Metsch B.: Quark models. Eur. Phys. J. A 35, 275 (2008)
Glozman L.Y., Plessas W., Varga K., Wagenbrunn R.F.: Unified description of light- and strange-baryon spectra. Phys. Rev. D 58, 094030 (1998)
Boffi S., Glozman L.Y., Klink W.H., Plessas W., Radici M., Wagenbrunn R.F.: Covariant electroweak nucleon form factors in a chiral constituent quark model. Eur. Phys. J. A 14, 17 (2002)
Krassnigg A., Schweiger W., Klink W.H.: Vector mesons in a relativistic point-form approach. Phys. Rev. C 67, 064003 (2003)
Kleinhappel, R.: Resonances and decay widths within relativistic point-from quantum mechanics. Master’s thesis, Karl-Franzens-Universität Graz (2010)
Sato T., Lee T.S.: Dynamical models of the excitations of nucleon resonances. J. Phys. G 36, 073001 (2009)
Murphy, K.C.: The structure of gluons in point form quantum chromodynamics. PhD thesis, University of Iowa (2009)
Author information
Authors and Affiliations
Corresponding author
Additional information
“Relativistic Description of Two- and Three-Body Systems in Nuclear Physics”, ECT*, October 19–23, 2009.
Rights and permissions
About this article
Cite this article
Biernat, E.P., Klink, W.H. & Schweiger, W. Point-Form Hamiltonian Dynamics and Applications. Few-Body Syst 49, 149–161 (2011). https://doi.org/10.1007/s00601-010-0102-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00601-010-0102-z