By Koch V.
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Extra resources for Aspects of chiral symmetry
7) we show the temperature dependence of the quark-condensate as predicted by the above formula. Currently, lattice gauge calculations predict a critical temperature Tc 150 MeV, above which the quark condensate has disappeared. At this temperature chiral perturbation theory predicts only a drop of about 50 %, which gets even smaller once pion masses are included . However, we do not expect chiral perturbation to work well close to the critical temperature. The strength of this approach is at low temperatures.
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Although this may true in some cases, one could easily imagine that one fixes the effective Lagrangian from some experiments and then is able to calculate other observables. For example, imagine that the effective pion-nucleon interaction has been fixed from pion nucleon-scattering experiments. g. the photo-production of pions. e. without any nucleons. As pointed out in the previous section, chiral invariance requires that the effective Lagrangian has to be build from structures involving U + U (142) such as tr(∂µ U + ∂ µ U ), tr(∂µ U + ∂ µ U )tr(∂µ U + ∂ µ U ), tr[(∂µ U + ∂ µ U )2 ], .
Aspects of chiral symmetry by Koch V.