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The Birman-Schwinger operator for the Cornell Hamiltonian

O Civitarese, S. Fassari, M. Gadella, F. Rinaldi

Abstract

Quantum Chromodynamics is the theory of strong interactions. It has been shown during the last decades that it describes correctly most of the properties of hadrons at high energy. The most distinctive feature of the theory is the realisation that the elementary particles which composed the known forms of matter, that is to say quarks and gluons, cannot be observed at low energy. In this work we are addressing this specific feature, known as confinement, by performing a rigorous mathematical treatment of the Cornell potential

The Birman-Schwinger operator for the Cornell Hamiltonian

Abstract

Quantum Chromodynamics is the theory of strong interactions. It has been shown during the last decades that it describes correctly most of the properties of hadrons at high energy. The most distinctive feature of the theory is the realisation that the elementary particles which composed the known forms of matter, that is to say quarks and gluons, cannot be observed at low energy. In this work we are addressing this specific feature, known as confinement, by performing a rigorous mathematical treatment of the Cornell potential
Paper Structure (8 sections, 90 equations)

This paper contains 8 sections, 90 equations.

Table of Contents

  1. Introduction
  2. The Hamiltonian
  3. The Birman-Schwinger method
  4. A physical bound for $||M||$
  5. Another estimation.
  6. First excited state.
  7. On the eigenfunctions
  8. Concluding Remarks