Linear $Σ$ Model in the Gaussian Functional Approximation

Details Linear $Σ$ Model in the Gaussian Functional Approximation Linear $Σ$ Model in the Gaussian Functional Approximation

2002-01-10

arxiv.org/abs/hep-th/0201064v1

Prog.Theor.Phys.106:1195-1212,2001

Physics

High Energy Physics

High Energy Physics - Theory

20 pages 9 figures

Scientific paper

10.1143/PTP.106.1195

We apply a self-consistent relativistic mean-field variational ``Gaussian functional'' (or Hartree) approximation to the linear $\sigma$ model with spontaneously and explicitly broken chiral O(4) symmetry. We set up the self-consistency, or ``gap'' and the Bethe-Salpeter equations. We check and confirm the chiral Ward-Takahashi identities, among them the Nambu-Goldstone theorem and the (partial) axial current conservation [CAC], both in and away from the chiral limit. With explicit chiral symmetry breaking we confirm the Dashen relation for the pion mass and partial CAC. We solve numerically the gap and Bethe-Salpeter equations, discuss the solutions' properties and the particle content of the theory.

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