Possible Effects of Fierz Transformations on Vacua of Some four Fermion Interaction Models

Bang Rong Zhou

doi:doi:10.11648/j.ijhep.20150201.11

| Peer-Reviewed

Possible Effects of Fierz Transformations on Vacua of Some four Fermion Interaction Models

Bang Rong Zhou

Published in International Journal of High Energy Physics (Volume 2, Issue 1)

Received: 23 December 2014 Accepted: 20 January 2015 Published: 1 February 2015

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

A theoretical research on possible effects of the Fierz transformations on the ground states (vacua) of some 2flavor four fermion (quark) interaction models has been systematically conducted. It has been shown that, based on the known criterions of the interplay between the antiquark-quark and diquark condensates, in 4D spacetime, for the given antiquark-quark channel couplings with chiral symmetry and from the heavy gluon exchange, the effects of the Fierz transformations are not enough to change the feature that the models’ vacua would be in the pure antiquark-quark condensate phases. However, for a given pure scalar diquark channel coupling with the strength HS, the Fierz transformations will lead to the nontrivial eﬀect that the model’s vacuum could be in the expected diquark condensate phase only if Nc<9 and HS is small, and as the increase of Nc and/or HS, the vacuum will get ﬁrst in a coexistence phase with diquark and antiquark-quark condensates then up to a pure antiquark-quark condensate phase until Nc goes to infinite. The similar conclusions are also drawn from relevant four fermion interaction models in 2D and 3D spacetime. The general significance of the research is indicated.

Published in	International Journal of High Energy Physics (Volume 2, Issue 1)
DOI	10.11648/j.ijhep.20150201.11
Page(s)	1-12
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Four Fermion Interactions, Fierz Transformations, Spinor and U(N) Space,Antiquark-Quark and Diquark Channels, Color Number Nc

References

[1]	Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961); 124, 246 (1961).
[2]	D.J. Gross and A. Neveu, Phys. Rev. D 10, 3235 (1974).
[3]	J. Goldstone, Nuovo Cimento 19, 154 (1961).
[4]	D. Weingarten, Phys. Rev. Lett. 51, 1830 (1983); S. Nussinov, Phys. Rev. Lett. 51, 2081 (1983); E. Witten, Phys. Rev. Lett. 51, 2351 (1983); C. Vafa and E. Witten, Nucl. Phys. B234, 173 (1984).
[5]	B. R. Zhou, Phys. Lett. B215, 364 (1988); B235, 412 (1990)(E); Zhou BangRong, Commun. Theor. Phys. 15, 319 (1991); 18, 347 (1992); 19, 377 (1993).
[6]	V. A. Miransky, Dynamical symmetry breaking in Quantum Field Theory, World Scientiﬁc, Singapore (1993) and the references therein.
[7]	D.A. Kirzhnits and A.D. Linde, Phys. Lett. B 42, 471 (1972); S. Weinberg, Phys. Rev. D 7, 2887 (1973); 9, 3357 (1974); L. Dolan and R. Jackew, Phys. Rev. D 9, 3320 (1974 ).
[8]	M.A. Sakawa and K. Yazaki, Nucl. Phys. A 504, 668 (1989); S.P. Klevansky, Rev. Mod. Phys. 64, 649 (1992); T. Hatsuda and T. Kunihiro, Phys. Rep. 247, 221 (1994).
[9]	D. Ebert, K.G. Klimenko, M.A. Vdovichenko, and A.S. Vshivtsev, Phys. Rev. D 61, 025005 (1999).
[10]	B. R. Zhou, Phys. Rev. D57, 3171 (1998); Phys. Lett. B444, 455 (1998); Zhou BangRong, Commun. Theor. Phys. 32, 425 (1999); 33, 451 (2000); 40, 67 (2003); 669 (2003); Wang XiaoMing and Zhou BangRong, ibid. 47, 1081 (2007).
[11]	J. C. Collins and M. J. Perry, Phys. Rev. Lett. 34, 1353 (1975); M. Alford, K. Rajagopal, and F. Wilczek, Phys. Lett. B422, 427 (1998); Nucl Phys . B537, 443 (1999); J. Berges and K. Rajagopal, Nucl. Phys. B538, 215 (1999).
[12]	R. Rapp, T. Sch fer, E. V. Shuryak, and M. Velkovsky, Phys. Rev. Lett. 81, 53 (1998).
[13]	M. Buballa, Phys. Rep. 407, 205 (2005).
[14]	D. Diakonov, H. Forkel, and M. Lutz, Phys. Lett. B 373, 147 (1996).
[15]	B. Vanderheyden and A.D. Jackson, Phys. Rev. D61, 076004 (2000).
[16]	S. B. Rüster and D. H. Rischke, Phys. Rev. D69, 045011 (2004).
[17]	Zhou BangRong, Commun. Theor. Phys. 47, 95 (2007); 520 (2007); 695 (2007).
[18]	Zhou BangRong, Commun. Theor. Phys. 51, 700 (2009).
[19]	W. Pauli, Nuovo Cimento 6, 205 (1957); F. Gürsey, ibid. 7, 411 (1958).
[20]	M. Peskin, Nucl. Phys. B175, 197 (1980).
[21]	D. Diakonov and V. Petrov, Diquarks in the instanton picture, in ’Quark cluster dynamics’, eds. K. Goeke et al., Springer-Verlag, 1993.
[22]	A. Smilga and J. J. M. Verbaarschot, Phys. Rev. D51, 829 (1995).
[23]	N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966); S. Coleman, Commun. Math. Phys. 31, 259 (1973).
[24]	Zhou BangRong, Commun. Theor. Phys. 54, 499 (2010)(E).

Cite This Article

Plain Text BibTeX RIS

APA Style

Bang Rong Zhou. (2015). Possible Effects of Fierz Transformations on Vacua of Some four Fermion Interaction Models. International Journal of High Energy Physics, 2(1), 1-12. https://doi.org/10.11648/j.ijhep.20150201.11

Copy | Download

ACS Style

Bang Rong Zhou. Possible Effects of Fierz Transformations on Vacua of Some four Fermion Interaction Models. Int. J. High Energy Phys. 2015, 2(1), 1-12. doi: 10.11648/j.ijhep.20150201.11

Copy | Download

AMA Style

Bang Rong Zhou. Possible Effects of Fierz Transformations on Vacua of Some four Fermion Interaction Models. Int J High Energy Phys. 2015;2(1):1-12. doi: 10.11648/j.ijhep.20150201.11

Copy | Download

@article{10.11648/j.ijhep.20150201.11,
  author = {Bang Rong Zhou},
  title = {Possible Effects of Fierz Transformations on Vacua of Some four Fermion Interaction Models},
  journal = {International Journal of High Energy Physics},
  volume = {2},
  number = {1},
  pages = {1-12},
  doi = {10.11648/j.ijhep.20150201.11},
  url = {https://doi.org/10.11648/j.ijhep.20150201.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhep.20150201.11},
  abstract = {A theoretical research on possible effects of the Fierz transformations on the ground states (vacua) of some 2flavor four fermion (quark) interaction models has been systematically conducted. It has been shown that, based on the known criterions of the interplay between the antiquark-quark and diquark condensates, in 4D spacetime, for the given antiquark-quark channel couplings with chiral symmetry and from the heavy gluon exchange, the effects of the Fierz transformations are not enough to change the feature that the models’ vacua would be in the pure antiquark-quark condensate phases. However, for a given pure scalar diquark channel coupling with the strength HS, the Fierz transformations will lead to the nontrivial eﬀect that the model’s vacuum could be in the expected diquark condensate phase only if Nc<9 and HS is small, and as the increase of Nc and/or HS, the vacuum will get ﬁrst in a coexistence phase with diquark and antiquark-quark condensates then up to a pure antiquark-quark condensate phase until Nc goes to infinite. The similar conclusions are also drawn from relevant four fermion interaction models in 2D and 3D spacetime. The general significance of the research is indicated.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Possible Effects of Fierz Transformations on Vacua of Some four Fermion Interaction Models
AU  - Bang Rong Zhou
Y1  - 2015/02/01
PY  - 2015
N1  - https://doi.org/10.11648/j.ijhep.20150201.11
DO  - 10.11648/j.ijhep.20150201.11
T2  - International Journal of High Energy Physics
JF  - International Journal of High Energy Physics
JO  - International Journal of High Energy Physics
SP  - 1
EP  - 12
PB  - Science Publishing Group
SN  - 2376-7448
UR  - https://doi.org/10.11648/j.ijhep.20150201.11
AB  - A theoretical research on possible effects of the Fierz transformations on the ground states (vacua) of some 2flavor four fermion (quark) interaction models has been systematically conducted. It has been shown that, based on the known criterions of the interplay between the antiquark-quark and diquark condensates, in 4D spacetime, for the given antiquark-quark channel couplings with chiral symmetry and from the heavy gluon exchange, the effects of the Fierz transformations are not enough to change the feature that the models’ vacua would be in the pure antiquark-quark condensate phases. However, for a given pure scalar diquark channel coupling with the strength HS, the Fierz transformations will lead to the nontrivial eﬀect that the model’s vacuum could be in the expected diquark condensate phase only if Nc<9 and HS is small, and as the increase of Nc and/or HS, the vacuum will get ﬁrst in a coexistence phase with diquark and antiquark-quark condensates then up to a pure antiquark-quark condensate phase until Nc goes to infinite. The similar conclusions are also drawn from relevant four fermion interaction models in 2D and 3D spacetime. The general significance of the research is indicated.
VL  - 2
IS  - 1
ER  -

Copy | Download

Author Information

Bang Rong Zhou

College of Physical Sciences, University of the Chinese Academy of Sciences, Beijing, China

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Bang Rong Zhou. (2015). Possible Effects of Fierz Transformations on Vacua of Some four Fermion Interaction Models. International Journal of High Energy Physics, 2(1), 1-12. https://doi.org/10.11648/j.ijhep.20150201.11

Copy | Download

ACS Style

Bang Rong Zhou. Possible Effects of Fierz Transformations on Vacua of Some four Fermion Interaction Models. Int. J. High Energy Phys. 2015, 2(1), 1-12. doi: 10.11648/j.ijhep.20150201.11

Copy | Download

AMA Style

Bang Rong Zhou. Possible Effects of Fierz Transformations on Vacua of Some four Fermion Interaction Models. Int J High Energy Phys. 2015;2(1):1-12. doi: 10.11648/j.ijhep.20150201.11

Copy | Download

@article{10.11648/j.ijhep.20150201.11,
  author = {Bang Rong Zhou},
  title = {Possible Effects of Fierz Transformations on Vacua of Some four Fermion Interaction Models},
  journal = {International Journal of High Energy Physics},
  volume = {2},
  number = {1},
  pages = {1-12},
  doi = {10.11648/j.ijhep.20150201.11},
  url = {https://doi.org/10.11648/j.ijhep.20150201.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhep.20150201.11},
  abstract = {A theoretical research on possible effects of the Fierz transformations on the ground states (vacua) of some 2flavor four fermion (quark) interaction models has been systematically conducted. It has been shown that, based on the known criterions of the interplay between the antiquark-quark and diquark condensates, in 4D spacetime, for the given antiquark-quark channel couplings with chiral symmetry and from the heavy gluon exchange, the effects of the Fierz transformations are not enough to change the feature that the models’ vacua would be in the pure antiquark-quark condensate phases. However, for a given pure scalar diquark channel coupling with the strength HS, the Fierz transformations will lead to the nontrivial eﬀect that the model’s vacuum could be in the expected diquark condensate phase only if Nc<9 and HS is small, and as the increase of Nc and/or HS, the vacuum will get ﬁrst in a coexistence phase with diquark and antiquark-quark condensates then up to a pure antiquark-quark condensate phase until Nc goes to infinite. The similar conclusions are also drawn from relevant four fermion interaction models in 2D and 3D spacetime. The general significance of the research is indicated.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Possible Effects of Fierz Transformations on Vacua of Some four Fermion Interaction Models
AU  - Bang Rong Zhou
Y1  - 2015/02/01
PY  - 2015
N1  - https://doi.org/10.11648/j.ijhep.20150201.11
DO  - 10.11648/j.ijhep.20150201.11
T2  - International Journal of High Energy Physics
JF  - International Journal of High Energy Physics
JO  - International Journal of High Energy Physics
SP  - 1
EP  - 12
PB  - Science Publishing Group
SN  - 2376-7448
UR  - https://doi.org/10.11648/j.ijhep.20150201.11
AB  - A theoretical research on possible effects of the Fierz transformations on the ground states (vacua) of some 2flavor four fermion (quark) interaction models has been systematically conducted. It has been shown that, based on the known criterions of the interplay between the antiquark-quark and diquark condensates, in 4D spacetime, for the given antiquark-quark channel couplings with chiral symmetry and from the heavy gluon exchange, the effects of the Fierz transformations are not enough to change the feature that the models’ vacua would be in the pure antiquark-quark condensate phases. However, for a given pure scalar diquark channel coupling with the strength HS, the Fierz transformations will lead to the nontrivial eﬀect that the model’s vacuum could be in the expected diquark condensate phase only if Nc<9 and HS is small, and as the increase of Nc and/or HS, the vacuum will get ﬁrst in a coexistence phase with diquark and antiquark-quark condensates then up to a pure antiquark-quark condensate phase until Nc goes to infinite. The similar conclusions are also drawn from relevant four fermion interaction models in 2D and 3D spacetime. The general significance of the research is indicated.
VL  - 2
IS  - 1
ER  -

Copy | Download