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Instantons are soliton solutions of "Euclidized" quantum field theories localized in space and time , especially the Yang-Mills equations in quantum chromodynamics after a Wick rotation from Minkowski space to four-dimensional Euclidean space . In all of these theories, instantons describe the quantum mechanical transition ( tunnel transition ) between the different classes of the vacuum state of the field under consideration and are said to be of great importance especially for the strong interaction in the low-energy range.

The instanton (as well as the anti-instanton) together with widely separated instanton-anti-instanton pairs mediate the tunneling process for the quantum mechanical ground state in the “double-well” potential (Euclidean time towards infinity). All excited states are mediated by periodic instantons (Euclidean time finite) - like all states in the case of the inverted “double-well” potential.

Instantons also provide an explanation for an important symmetry breaking : they can change the handedness of elementary particles in the quantum chromodynamics vacuum. The associated chiral symmetry plays a central role in the physics of hadrons . Instantons are also used in the “ inflaton field ” of cosmology to explain the inflationary phase transition in the early days of the universe.


  • Marcus Hutter : Instantons in the QCD , dissertation, 1995.
  • R. Rajaraman: Solitons and instantons - an introduction to solitons and instantons in quantum field theory. Elsevier, Amsterdam 2005, ISBN 0-444-87047-4
  • Mikhail A. Shifman: Instantons in gauge theories. World Scientific, Singapore 1994, ISBN 981-02-1681-5
  • Sidney Coleman : Aspects of Symmetry , Cambridge University Press, 1985, ISBN 0-521-31827-0

Individual evidence

  1. Harald JW Müller-Kirsten, Introduction to Quantum Mechanics: Schrödinger Equation and Path Integral, 2nd ed., World Scientific, 2012, ISBN 978-981-4397-73-5 .