Criterion for dynamical chiral symmetry breaking
arXiv:hep-th/0703050 · doi:10.1103/PhysRevD.76.025020
Abstract
The Bethe-Salpeter equation is related to a generalized quantum-mechanical Hamiltonian. Instability of the presumed vacuum, indicated by a tachyon, is related to a negative energy eigenstate of this Hamiltonian. The variational method shows that an arbitrarily weak long-range attraction leads to chiral symmetry breaking, except in the scale-invariant case when the instability occurs at a critical value of the coupling. In the case of short-range attraction, an upper bound for the critical coupling is obtained.
10 pages, 2 figures; made minor changes, published version