Few-Body Systems

, Volume 54, Issue 12, pp 2283–2301 | Cite as

Scalar-Particle Self-Energy Amplitudes and Confinement in Minkowski Space

  • Elmar P. Biernat
  • Franz Gross
  • Teresa Peña
  • Alfred StadlerEmail author


We analyze the analytic structure of the Covariant Spectator Theory (CST) contribution to the self-energy amplitude for a scalar particle in a \({\phi^2\chi}\) theory. To this end we derive dispersion relations in 1+1 and in 3+1 dimensional Minkowski space. The divergent loop integrals in 3+1 dimensions are regularized using dimensional regularization. We find that the CST dispersion relations exhibit, in addition to the usual right-hand branch cut, also a left-hand cut. The origin of this “spectator” left-hand cut can be understood in the context of scattering for a scalar \({\phi^2\chi^2}\) -type theory. If the interaction kernel contains a linear confining component, its contribution to the self-energy vanishes exactly.


Dispersion Relation Scalar Particle Dimensional Regularization Chiral Limit Compress Baryonic Matter 
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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Elmar P. Biernat
    • 1
  • Franz Gross
    • 2
    • 3
  • Teresa Peña
    • 1
  • Alfred Stadler
    • 4
    • 5
    Email author
  1. 1.CFTP (Centro de Física Teórica de Partículas), Instituto Superior TécnicoUniversidade Técnica de LisboaLisboaPortugal
  2. 2.Thomas Jefferson National Accelerator FacilityNewport NewsUSA
  3. 3.College of William and MaryWilliamsburgUSA
  4. 4.Departamento de Física daUniversidade deÉvoraÉvoraPortugal
  5. 5.Centro de Física Nuclear da Universidade de LisboaLisboaPortugal

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