SU(N) Instantons in the Field Strength Approach to QCD

  • H. Reinhardt


Field strength formulated Yang-Mills theory is confronted to the traditional formulation in terms of gauge fields. It is shown that both formulations yield the same semiclassics, in particular the same instanton physics. The field strength formulation is, however, superior at the tree level where it includes already a good deal of quantum fluctuations of the standard formulation. These quantum fluctuations break the scale invariance of classical QCD and give rise to an instanton interaction. The latter causes the instanton to condense and to form a homogeneous instanton solid. These instanton solids show up in the field strength approach as homogeneous (constant up to gauge transformations) vacuum solutions. A new class of SU(N) instantons is presented which are not embeddings of SU(N-1) instantons but have non-trivial SU(N) color structure and carry winding number \(n = \frac{N}{6}({N^2} - 1)\). These novel instantons generate (after condensation) the lowest action homogeneous solutions of the field strength approach.


Field Strength Gauge Group Chiral Symmetry Gauge Field Gauge Potential 
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© Springer Science+Business Media New York 1994

Authors and Affiliations

  • H. Reinhardt
    • 1
  1. 1.Institut für Theoretische PhysikUniversität TübingenTübingenGermany

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