Weekly Bulletin

In quantum chromodynamics, without interactions, quarks have no mass and a conserved quantity called chirality. In reality, quarks have mass and chiral symmetry is broken. This is thought to be the result of spontaneous symmetry breaking by the interaction. In this talk we consider a lattice version of the Nambu-Jona-Lasinio model with interacting staggered fermions in the Kogut-Susskind Hamiltonian formalism. In a strong coupling regime for the four-fermion interaction, we prove that the mass of the fermions is spontaneously generated at sufficiently low temperatures. This implies that the chiral symmetry is spontaneously broken if the continuum limit exists. For the proof, the reflection positivity for fermions and the infrared bound method are crucial. This talk is based on joint work with Tohru Koma.