Possible Effects of Fierz Transformations on Vacua of Some four Fermion Interaction Models
Issue:
Volume 2, Issue 1, February 2015
Pages:
1-12
Received:
23 December 2014
Accepted:
20 January 2015
Published:
1 February 2015
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.
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 ant...
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