On the rotator Hamiltonian for the SU$(N)\times\,$SU$(N)$ sigma-model in the delta-regime
| Autor: | Ferenc Niedermayer, Peter Weisz, Janos Balog |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Delta
Physics High Energy Physics - Theory Sigma model 010308 nuclear & particles physics General Physics and Astronomy FOS: Physical sciences 01 natural sciences symbols.namesake High Energy Physics - Theory (hep-th) 0103 physical sciences symbols 010306 general physics Hamiltonian (quantum mechanics) Mathematical physics |
| Zdroj: | Progress of Theoretical and Experimental Physics |
| DOI: | 10.48550/arxiv.1912.05232 |
| Popis: | 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 $\ell=L_t/L\to\infty\,.$ 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 $N=3\,.$ Comment: 36 pages, 2 figures |
| Databáze: | OpenAIRE |
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