A free action for pions as quark composites
Abstract
In the framework of an approach to bosonization based on the use of fermionic composites as fundamental variables, a quadratic action in even Grassmann variables with the quantum numbers of the pions has been constructed. It includes the sigma-field in order to be invariant under SU(2)_L times SU(2)]_R transformations over the quarks. This action exhibits the Goldstone phenomenon reducing its symmetry to the O(3) isospin invariance. A squared mass for the pions is generated according to PCAC. The model has been investigated in the Stratonovitch-Hubbard representation, in which form it is reminiscent of the Gell-Mann-Levy model. By the saddle point method a renormalizable expansion in inverse powers of the index of nilpotency of the mesonic fields (which is 24), is generated. The way it might be used in a new perturbative approach to QCD is outlined.
Cite
@article{arxiv.hep-ph/9801389,
title = {A free action for pions as quark composites},
author = {Sergio Caracciolo and Fabrizio Palumbo},
journal= {arXiv preprint arXiv:hep-ph/9801389},
year = {2009}
}
Comments
18 pages, accepted for publication on Nuclear Physics B