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arXiv · hep-ph/9801389

A free action for pions as quark composites

Sergio Caracciolo·Fabrizio Palumbo
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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.

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Sergio Caracciolo, Fabrizio Palumbo. 1998-01-22. A free action for pions as quark composites. https://doi.org/10.1016/s0550-3213(97)00680-9

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