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Weak solution method of the non-perturbative renormalization group equation to describe dynamical chiral symmetry breaking and its application to beyond the ladder analysis in QCD
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The method of non-perturbative renormalization group (NPRG) is applied to the analysis of dynamical chiral symmetry breaking (DCSB) in QCD. We show that the DCSB solution of the NPRG flow equation can be obtained without the bosonization. The solution, having the singular point, can be authorized as the weak solution of partial differential equation, and can be easily evaluated using the method of the characteristic curve. Also we show that our non-ladder extended approximation improves almost perfectly the gauge dependence of the chiral condensates.
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Fermions and the Renormalisation Group at Large N
At large N, fermionic quantum field theories have exact effective actions depending only on flavour-singlet fermion bilinears, making the local potential approximation exact and yielding new conformal fixed points.
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