Planar Yang-Mills theory: Hamiltonian, regulators and mass gap

Dimitra Karabali, Chanju Kim, V. P. Nair

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Abstract

We carry out the Hamiltonian analysis of non-Abelian gauge theories in (2+1) dimensions in a gauge-invariant matrix parametrization of the fields. A detailed discussion of regularization issues and the construction of the renormalized Laplace operator on the configuration space, which is proportional to the kinetic energy, are given. The origin of the mass gap is analyzed and the lowest eigenstates of the kinetic energy are explicitly obtained; these have zero charge and exhibit a mass gap. The nature of the corrections due to the potential energy, the possibility of an improved perturbation theory and a Schrödinger-like equation for the states are also discussed.

Original languageEnglish
Pages (from-to)661-694
Number of pages34
JournalNuclear Physics, Section B
Volume524
Issue number3
DOIs
StatePublished - 3 Aug 1998

Bibliographical note

Funding Information:
This work was supported in part by the National Science Foundation grant PHY-9322591 and by the Department of Energy grant DE-FG02-91ER40651-Task B. C.K.'s work was supported in part by the Korea Science and Engineering Foundation through the SRC program. We thank B. Sakita for many useful discussions. C.K. also thanks the Physics Department of the City College of the CUNY where part of the work was done.

Keywords

  • Glueballs
  • Mass gap
  • Yang-Mills

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