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 σfield in order to be invariant under [ SU(2)] _{L} ⊗ [ 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 StratonovitchHubbard representation, in which form it is reminiscent of the GellMannLévy model. By the saddlepoint 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.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1998
 DOI:
 10.1016/S05503213(97)006809
 arXiv:
 arXiv:hepph/9801389
 Bibcode:
 1998NuPhB.512..505C
 Keywords:

 High Energy Physics  Phenomenology;
 High Energy Physics  Lattice;
 High Energy Physics  Theory
 EPrint:
 18 pages, accepted for publication on Nuclear Physics B