FUN WITH DIRAC EIGENVALUES.

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It is popular to discuss low energy physics in lattice gauge theory ill terms of the small eigenvalues of the lattice Dirac operator. I play with some ensuing pitfalls in the interpretation of these eigenvalue spectra. In short, thinking about the eigenvalues of the Dirac operator in the presence of gauge fields can give some insight, for example the elegant Banks-Casher picture for chiral symmetry breaking. Nevertheless, care is necessary because the problem is highly non-linear. This manifests itself in the non-intuitive example of how adding flavors enhances rather than suppresses low eigenvalues. Issues involving zero mode suppression represent one ... continued below

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10 pages

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CREUTZ, M. January 26, 2006.

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It is popular to discuss low energy physics in lattice gauge theory ill terms of the small eigenvalues of the lattice Dirac operator. I play with some ensuing pitfalls in the interpretation of these eigenvalue spectra. In short, thinking about the eigenvalues of the Dirac operator in the presence of gauge fields can give some insight, for example the elegant Banks-Casher picture for chiral symmetry breaking. Nevertheless, care is necessary because the problem is highly non-linear. This manifests itself in the non-intuitive example of how adding flavors enhances rather than suppresses low eigenvalues. Issues involving zero mode suppression represent one facet of a set of connected unresolved issues. Are there non-perturbative ambiguities in quantities such as the topological susceptibility? How essential are rough gauge fields, i.e. gauge fields on which the winding number is ambiguous? How do these issues interplay with the quark masses? I hope the puzzles presented here will stimulate more thought along these lines.

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10 pages

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  • SENSE OF BEAUTY IN PHYSICS; UNIVERSITY OF PISA, ITALY; 20060126 through 20060127

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  • Report No.: BNL--75285-2005-CP
  • Grant Number: DE-AC02-98CH10886
  • Office of Scientific & Technical Information Report Number: 862308
  • Archival Resource Key: ark:/67531/metadc794726

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • January 26, 2006

Added to The UNT Digital Library

  • Dec. 19, 2015, 7:14 p.m.

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  • Dec. 12, 2016, 8:11 p.m.

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CREUTZ, M. FUN WITH DIRAC EIGENVALUES., article, January 26, 2006; [Upton, New York]. (digital.library.unt.edu/ark:/67531/metadc794726/: accessed January 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.