Abstract
A number of exactly integrable (quark) models of quantum field theory that feature an infinite correlation length are considered. An instability of the standard vacuum quark ensemble, a Dirac sea (in spacetimes of dimension higher than three), is highlighted. It is due to a strong ground-state degeneracy, which, in turn, stems from a special character of the energy distribution. In the case where the momentumcutoff parameter tends to infinity, this distribution becomes infinitely narrow and leads to large (unlimited) fluctuations. A comparison of the results for various vacuum ensembles, including a Dirac sea, a neutral ensemble, a color superconductor, and a Bardeen–Cooper–Schrieffer (BCS) state, was performed. In the presence of color quark interaction, a BCS state is unambiguously chosen as the ground state of the quark ensemble.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. D. Faddeev, Theor. Math. Phys. 148, 986 (2006).
L. V. Keldysh, Doctoral (Phys. Math.) Dissertation (Phys. Inst. of Acad. Sci., Moscow, 1965); E. O. Kane, Phys. Rev. 131, 79 (1963); V. L. Bonch-Bruevich, in Solid State Physics, Collection of Articles (VINITI, Moscow, 1965) [in Russian].
W. Thirring, Ann. Phys. (N. Y.) 3, 91 (1958);J. M. Luttinger, J. Math. Phys. 4, 1154 (1963); D. C. Mattis and E. H. Lieb, J. Math. Phys. 6, 304 (1965).
G. M. Zinovjev and S. V. Molodtsov, Theor. Math Phys. 160, 1238 (2009); S. V. Molodtsov and G. M. Zinovjev, Phys. Rev. D 80, 076001 (2009); S. V. Molodtsov and G. M. Zinovjev, Phys. Rev. D 80, 076001 (2009); S. V. Molodtsov, A. N. Sissakian, and G. M. Zinovjev, Europhys. Lett. 87, 61001 (2009).
J. V. Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932) [in German].
T. Fujita, M. Hiramoto, and H. Takahashi, in Focus on Boson Research (Nova Science, New York, 2005).
Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961).
S. V. Molodtsov and G. M. Zinovjev, Europhys. Lett. 93, 11001 (2011); Phys. Rev. D 84, 036011 (2011); G. M. Zinovjev and S. V. Molodtsov, Phys. At. Nucl. 75, 239 (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © G.M. Zinovjev, S.V. Molodtsov, 2016, published in Yadernaya Fizika, 2016, Vol. 79, No. 2, pp. 166–173.
Rights and permissions
About this article
Cite this article
Zinovjev, G.M., Molodtsov, S.V. Fluctuation instability of the Dirac Sea in quark models of strong interactions. Phys. Atom. Nuclei 79, 278–284 (2016). https://doi.org/10.1134/S106377881602023X
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S106377881602023X