Use of even Grassmann variables to construct effective actions for mesons

Details Use of even Grassmann variables to construct effective actions for mesons Use of even Grassmann variables to construct effective actions for mesons

1998-02-05

arxiv.org/abs/hep-lat/9802002v1

Nucl.Phys.Proc.Suppl. 63 (1998) 790-792

Physics

High Energy Physics

High Energy Physics - Lattice

Talk presented at Lattice '97 (Theoretical Developments), Edinburgh (UK), July 1997. LaTeX2e, 3 pages, uses espcrc2

Scientific paper

10.1016/S0920-5632(97)00901-8

A quadratic action in even Grassmann variables with the quantum numbers of the pions has been studied. 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. 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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