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تسجيل مستخدم جديدOn the rotator Hamiltonian for the SU$(N)times,$SU$(N)$ sigma-model in the delta-regime
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We investigate some properties of the standard rotator approximation of the SU$(N)times,$SU$(N)$ sigma-model in the delta-regime. In particular we show that the isospin susceptibility calculated in this framework agrees with that computed by chiral perturbation theory up to next-to-next to leading order in the limit $ell=L_t/Ltoinfty,.$ The difference between the results involves terms vanishing like $1/ell,,$ plus terms vanishing exponentially with $ell,$. As we have previously shown for the O($n$) model, this deviation can be described by a correction to the rotator spectrum proportional to the square of the quadratic Casimir invariant. Here we confront this expectation with analytic nonperturbative results on the spectrum in 2 dimensions for $N=3,.$
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In a previous paper we found that the isospin susceptibility of the O($n$) sigma-model calculated in the standard rotator approximation differs from the next-to-next to leading order chiral perturbation theory result in terms vanishing like $1/ell,,$
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