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arXiv · hep-lat/9802002

Use of even Grassmann variables to construct effective actions for mesons

Sergio Caracciolo·Fabrizio Palumbo
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Abstract

A quadratic action in even Grassmann variables with the quantum numbers of the pions has been studied. It includes the $σ$-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. 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. 1998-02-05. Use of even Grassmann variables to construct effective actions for mesons. https://doi.org/10.1016/s0920-5632(97)00901-8

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