Application of Non-Perturbative Renormalization Group to Nambu-Jona-Lasinio/Gross-Neveu model at Finite Temperature and Chemical Potential

The chiral phase structure of the Nambu-Jona-Lasinio/Gross-Neveu model at finite temperature T and finite chemical potential \mu is investigated using (Wilsonian) Non-Perturbative Renormalization Group (NPRG). In the large N_c limit, the solutions of NPRG with various cutoff schemes are shown. For a sufficiently large ultra-violet cutoff, NPRG results coincide with those of Schwinger-Dyson equation and have little cutoff scheme dependence. Next, to improve the approximation, we incorporate the mesonic fluctuations. We introduce the auxiliary fields for mesons, and then derive NPRG equation for finite N_c. The chiral phase structure on (T,\mu) plane beyond the leading of 1/N_c expansion is investigated in the sharp cutoff limit. N_c dependence of chiral phase diagram is obtained.Comment: 21 pages, 10 epsf figures, to be published in Progress of Theoretical Physic

The effectiveness of the local potential approximation in the Wegner-Houghton renormalization group

The non-perturbative Wegner-Houghton renormalization group is analyzed by the local potential approximation in O(N) scalar theories in d-dimensions $(3\leq d\leq 4)$. The leading critical exponents \nu are calculated in order to investigate the effectiveness of the local potential approximation by comparing them with the other non-perturbative methods. We show analytically that the local potential approximation gives the exact exponents up to $O(\epsilon )$ in \epsilon-expansion and the leading in 1/N-expansion. We claim that this approximation offers fairly accurate results in the whole range of the parameter space of N and d. It is a great advantage of our method that no diverging expansions appear in the procedure.Comment: 13 pages, latex, 6 figure

Wilson Renormalization Group Equations for the Critical Dynamics of Chiral Symmetry

The critical dynamics of the chiral symmetry breaking induced by gauge interaction is examined in the Wilson renormalization group framework in comparison with the Schwinger-Dyson approach. We derive the beta functions for the four-fermi couplings in the sharp cutoff renormalzation group scheme, from which the critical couplings and the anomalous dimensions of the fermion composite operators near criticality are immediately obtained. It is also shown that the beta functions lead to the same critical behavior found by solving the so-called ladder Schwinger-Dyson equation, if we restrict the radiative corrections to a certain limited type.Comment: 13 pages, 7 epsf figure

Rapidly Converging Truncation Scheme of the Exact Renormalization Group

The truncation scheme dependence of the exact renormalization group equations is investigated for scalar field theories in three dimensions. The exponents are numerically estimated to the next-to-leading order of the derivative expansion. It is found that the convergence property in various truncations in the number of powers of the fields is remarkably improved if the expansion is made around the minimum of the effective potential. It is also shown that this truncation scheme is suitable for evaluation of infrared effective potentials. The physical interpretation of this improvement is discussed by considering O(N) symmetric scalar theories in the large-N limit.Comment: 17 pages including 13 figures, LaTeX, to appear in Prog. Theor. Phys., references adde

非摂動繰り込み群の定式化と素粒子物理への応用

取得学位：博士(理学)，学位授与番号：博甲第199号，学位授与年月日：平成9年3月25日,学位授与年：199