Abc of instantons

A. I. Valnshteln; V. I. Zakharov; V. A. Novikov; M. A. Shifman

doi:10.1070/PU1982v025n04ABEH004533

Abc of instantons

A. I. Valnshteln, V. I. Zakharov, V. A. Novikov, M. A. Shifman

Physics and Astronomy (Twin Cities)

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221 Scopus citations

Abstract

An attempt is made to present an instanton "calculus" in a relatively simple form. The physical meaning of instantons is explained by the example of the quantum-mechanical problem of energy levels in a two-humped potential. The nonstandard solution to this problem based on instantons is analyzed and the reader is acquainted with the main technical elements used in this approach. Instantons in quantum chromodynamics are then considered. The Euclidean formulation of the theory is described. Classical solutions of the field equations (the Belavin-Polyakov-Shvarts- Tyupkin instantons) are obtained explicitly and their properties are studied. The calculation of the instanton density is described and the complete result is given for an arbitrary number of colors. The effects associated with fermion fields are briefly described.

Original language	English (US)
Pages (from-to)	195-215
Number of pages	21
Journal	Soviet Physics - Uspekhi
Volume	25
Issue number	4
DOIs	https://doi.org/10.1070/PU1982v025n04ABEH004533
State	Published - Apr 30 1982

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title = "Abc of instantons",

abstract = "An attempt is made to present an instanton {"}calculus{"} in a relatively simple form. The physical meaning of instantons is explained by the example of the quantum-mechanical problem of energy levels in a two-humped potential. The nonstandard solution to this problem based on instantons is analyzed and the reader is acquainted with the main technical elements used in this approach. Instantons in quantum chromodynamics are then considered. The Euclidean formulation of the theory is described. Classical solutions of the field equations (the Belavin-Polyakov-Shvarts- Tyupkin instantons) are obtained explicitly and their properties are studied. The calculation of the instanton density is described and the complete result is given for an arbitrary number of colors. The effects associated with fermion fields are briefly described.",

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T1 - Abc of instantons

AU - Valnshteln, A. I.

AU - Zakharov, V. I.

AU - Novikov, V. A.

AU - Shifman, M. A.

PY - 1982/4/30

Y1 - 1982/4/30

N2 - An attempt is made to present an instanton "calculus" in a relatively simple form. The physical meaning of instantons is explained by the example of the quantum-mechanical problem of energy levels in a two-humped potential. The nonstandard solution to this problem based on instantons is analyzed and the reader is acquainted with the main technical elements used in this approach. Instantons in quantum chromodynamics are then considered. The Euclidean formulation of the theory is described. Classical solutions of the field equations (the Belavin-Polyakov-Shvarts- Tyupkin instantons) are obtained explicitly and their properties are studied. The calculation of the instanton density is described and the complete result is given for an arbitrary number of colors. The effects associated with fermion fields are briefly described.

AB - An attempt is made to present an instanton "calculus" in a relatively simple form. The physical meaning of instantons is explained by the example of the quantum-mechanical problem of energy levels in a two-humped potential. The nonstandard solution to this problem based on instantons is analyzed and the reader is acquainted with the main technical elements used in this approach. Instantons in quantum chromodynamics are then considered. The Euclidean formulation of the theory is described. Classical solutions of the field equations (the Belavin-Polyakov-Shvarts- Tyupkin instantons) are obtained explicitly and their properties are studied. The calculation of the instanton density is described and the complete result is given for an arbitrary number of colors. The effects associated with fermion fields are briefly described.

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Abc of instantons

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