Auxiliary field method in 4- and 3-dimensional Nambu–Jona-Lasinio models

Taro Kashiwa; Tomohiko Sakaguchi

doi:10.1103/PhysRevD.68.065002

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Auxiliary field method in 4- and 3-dimensional Nambu–Jona-Lasinio models

Taro Kashiwa^*

Tomohiko Sakaguchi^†

Department of Physics, Ehime University, Matsuyama 790-8577, Japan

Department of Physics, Kyushu University, Fukuoka 812-8581, Japan

^*Electronic address: kashiwa@phys.sci.ehime-u.ac.jp
^†Electronic address: tomohiko@higgs.phys.kyushu-u.ac.jp

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Phys. Rev. D 68, 065002 – Published 3 September, 2003

DOI: https://doi.org/10.1103/PhysRevD.68.065002

Abstract

In order to check the validity of the auxiliary field method in the Nambu–Jona-Lasinio model, the one-loop (= quantum) effects of auxiliary fields on the gap equation are considered with N-component fermion models in four and three dimensions. N is not assumed very large but is regarded as a loop expansion parameter. To overcome infrared divergences caused by the Nambu-Goldstone bosons, an intrinsic fermion mass is assumed. It is shown that the loop expansion can be justified by this intrinsic mass whose lower limit is also given. It is found that due to quantum effects, chiral symmetry breaking (χSB) is restored in $D = 4$ and $D = 3$ when the four-Fermi coupling is large. However, χSB is enhanced in a small coupling region in $D = 3.$

References (17)

Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961).
S. P. Klevansky and R. H. Lemmer, Phys. Rev. D 39, 3478 (1989).
V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, Phys. Rev. D 52, 4718 (1995); ibid.G. W. Semenoff, I. A. Shovkovy, and L. C. R. Wijewardhana, 60, 105024 (1999).
M. Ishii, T. Kashiwa, and N. Tanimura, Prog. Theor. Phys. 100, 353 (1998).
M. Ishii, T. Kashiwa, and N. Tanimura, Phys. Rev. D 65, 065025 (2002).
T. Inagaki, T. Muta, and S. D. Odintsov, Mod. Phys. Lett. A 8, 2117 (1993); ibid.B. Geyer, L. N. Granda, and S. D. Odintsov, 11, 2053 (1996).
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See, for example, E. Fradkin, Field Theories of Condensed Matter Systems (Addison-Wesley, New York, 1991), p. 327.
T. Kashiwa, Y. Ohnuki, and M. Suzuki, Path Integral Methods (Clarendon, Oxford, 1997), p. 162.
T. Kashiwa, Phys. Rev. D 59, 085002 (1999).
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T. Kashiwa and T. Sakaguchi, hep-th/0301019.

[c1] Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961).

[c2] S. P. Klevansky and R. H. Lemmer, Phys. Rev. D 39, 3478 (1989).

[c3] V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, Phys. Rev. D 52, 4718 (1995); ibid.G. W. Semenoff, I. A. Shovkovy, and L. C. R. Wijewardhana, 60, 105024 (1999).

[c4] M. Ishii, T. Kashiwa, and N. Tanimura, Prog. Theor. Phys. 100, 353 (1998).

[c5] M. Ishii, T. Kashiwa, and N. Tanimura, Phys. Rev. D 65, 065025 (2002).

[c6] T. Inagaki, T. Muta, and S. D. Odintsov, Mod. Phys. Lett. A 8, 2117 (1993); ibid.B. Geyer, L. N. Granda, and S. D. Odintsov, 11, 2053 (1996).

[c7] D. Gross and A. Neveu, Phys. Rev. D 10, 3235 (1974); T. Kugo, Prog. Theor. Phys. 55, 2032 (1976); ibid.K. Kikkawa, 56, 947 (1976).

[c8] See, for example, E. Fradkin, Field Theories of Condensed Matter Systems (Addison-Wesley, New York, 1991), p. 327.

[c9] T. Kashiwa, Y. Ohnuki, and M. Suzuki, Path Integral Methods (Clarendon, Oxford, 1997), p. 162.

[c10] T. Kashiwa, Phys. Rev. D 59, 085002 (1999).

[c11] H. Kleinert and B. Van den Bossche, Phys. Lett. B 474, 336 (2000).

[c12] H. Kleinert and E. Babeav, Phys. Lett. B 438, 311 (1998).

[c13] E. Babaev, Phys. Rev. D 62, 074020 (2000); T. Lee and Y. Oh, Phys. Lett. B 475, 207 (2000).

[c14] H. J. He, Y. P. Kuang, Q. Wang, and Y. P. Yi, Phys. Rev. D 45, 4610 (1992).

[c15] E. N. Nikolov, W. Broniowski, C. V. Christov, G. Ripka, and K. Goeke, Nucl. Phys. A608, 411 (1996).

[c16] T. W. Appelquist, M. Bowick, D. Karabali, and L. C. R. Wijewardhana, Phys. Rev. D 33, 3704 (1986).

[c17] T. Kashiwa and T. Sakaguchi, hep-th/0301019.

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Auxiliary field method in 4- and 3-dimensional Nambu–Jona-Lasinio models

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