Gap Equations from Fermionic Constraints on the Light-Front

We investigate how the gap equations are obtained in the light-front formalism within the four-Fermi theories. Instead of the zero-mode constraint, we find that the "fermionic constraints" on nondynamical spinor components are responsible for symmetry breaking. Careful treatment of the infrared divergence is indispensable for obtaining the gap equation.Comment: 7 pages, LaTeX, reduced and modified version of hep-th/960806

Color Glass Condensate in QCD at High Energy

I give a brief review about the color glass condensate, which is the universal form of hadrons and nuclei at high energies.Comment: 4 pages, talk presented at ICHEP2004, Beijing, China, August 2004, minor modificatio

Anatomy of the magnetic catalysis by renormalization-group method

We first examine the scaling argument for a renormalization-group (RG) analysis applied to a system subject to the dimensional reduction in strong magnetic fields, and discuss the fact that a four-Fermi operator of the low-energy excitations is marginal irrespective of the strength of the coupling constant in underlying theories. We then construct a scale-dependent effective four-Fermi interaction as a result of screened photon exchanges at weak coupling, and establish the RG method appropriately including the screening effect, in which the RG evolution from ultraviolet to infrared scales is separated into two stages by the screening-mass scale. Based on a precise agreement between the dynamical mass gaps obtained from the solutions of the RG and Schwinger-Dyson equations, we discuss an equivalence between these two approaches. Focusing on QED and Nambu--Jona-Lasinio model, we clarify how the properties of the interactions manifest themselves in the mass gap, and point out an importance of respecting the intrinsic energy-scale dependences in underlying theories for the determination of the mass gap. These studies are expected to be useful for a diagnosis of the magnetic catalysis in QCD.Comment: 8 pages, 3 figures, version published in PL