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 TMF, 2006, Volume 146, Number 2, Pages 267–298 (Mi tmf2035)

Instanton in the Field of a Pointlike Source of a Euclidean Non-Abelian Field

G. M. Zinovjeva, S. V. Molodtsovbc

a N. N. Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
c Joint Institute for Nuclear Research

Abstract: We consider the behavior of an (anti)instanton in the field of a pointlike source of a Euclidean non-Abelian field and investigate (anti)instanton deformations described by variations of its characteristic parameters. We formulate the variational problem of seeking the corresponding “crumpled” topological configurations and solve it algebraically using the Ritz method (of multipole decomposition of deformation fields). We investigate the domain of parameters specific for the instanton liquid model. We propose a simple method of taking contributions of such configurations in the functional integral into account approximately. In the framework of superposition analysis, we obtain an estimate for the mean energy of the source in the instanton liquid, and the estimate increases linearly with distance. In the case of a dipole in the color-singlet state, the energy is a linear function of the distance between the sources with thesources with the “strength” coefficient agreeing well with the known model and lattice estimates.

Keywords: instanton, external field, approximate solution, deformations

DOI: https://doi.org/10.4213/tmf2035

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English version:
Theoretical and Mathematical Physics, 2006, 146:2, 221–247

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Revised: 04.06.2005

Citation: G. M. Zinovjev, S. V. Molodtsov, “Instanton in the Field of a Pointlike Source of a Euclidean Non-Abelian Field”, TMF, 146:2 (2006), 267–298; Theoret. and Math. Phys., 146:2 (2006), 221–247

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf2035
• https://doi.org/10.4213/tmf2035
• http://mi.mathnet.ru/eng/tmf/v146/i2/p267

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Zinovjev GM, Molodtsov SV, “Screening of a color field in an instanton liquid”, Physics of Atomic Nuclei, 70:6 (2007), 1136–1145
2. Zinovjev GM, Molodtsov SV, Siemiarczuk T, et al., “Sigma meson and phonon-like excitations of the instanton vacuum”, Physics of Atomic Nuclei, 71:2 (2008), 313–320
3. Molodtsov, SV, “Towards light scalar meson structure”, European Physical Journal C, 61:1 (2009), 61
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