Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-01-22
Nucl.Phys. B512 (1998) 505-519; Erratum-ibid. B555 (1999) 656
Physics
High Energy Physics
High Energy Physics - Phenomenology
18 pages, accepted for publication on Nuclear Physics B
Scientific paper
10.1016/S0550-3213(97)00680-9
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.
Caracciolo Sergio
Palumbo Fabrizio
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