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Mathematical aspects of ‘t Hooft’s eigenvalue problem in two-dimensional quantum chromodynamics

Part I. A variational approach, and nodal properties of the eigenfunctions

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Abstract

We consider the eigenvalue problem of t′ Hooft for the meson spectrum in 2-dimensional QCD. Various alternative formulations are discussed, and their equivalence is proved. Then, a variational characterization of the eigenfunctions and the eigenvalues is derived yielding that the spectrum is discrete and consists of denumerably many positive eigenvalues tending to infinity. The corresponding eigenfunctions are real analytic, and form a complete system in L2 Finally, the number of nodes of each eigenfunctions is estimated.

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Authors and Affiliations

  1. Mathematisches Institut der Universität, Wegelerstraße 10, D-5300, Bonn

    Stefan Hildebrandt

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  1. Stefan Hildebrandt
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Additional information

This work has been supported by the Sonderforschungsbereich 72 at the University of Bonn.

The author would like to thank Josef Bemelmans for several discussions, Bernd Schmidt and Tony Tromba for critical remarks about the first draft of the manuscript (April 1977), and, in particular, Vladimir Višnjić for introducing him to the problem, and for explaining the physical background.

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Hildebrandt, S. Mathematical aspects of ‘t Hooft’s eigenvalue problem in two-dimensional quantum chromodynamics. Manuscripta Math 24, 45–79 (1978). https://doi.org/10.1007/BF01168562

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  • DOI: https://doi.org/10.1007/BF01168562

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