Dynamical Parity Violation in the Two-Dimensional Yukawa Theory

The strong coupling regime and phase structure of the two-dimensional field theory with the Yukawa coupling and boson self-interaction are investigated by means of the methods of canonical transformations and renormalization group. The phase diagram in the (Y, G)-plane is constructed, where Y and G are Yukawa and self-interaction coupling constants. The Hamiltonians describing the system in each phase are obtained. It is shown that the parity is dynamically broken and massive necessarily, if G >> Y. In the case of the pure Yukawa interaction (G ≡ 0), there are two different phases (symmetric and with broken symmetry) which have very close free energy densities. However, the symmetric phase is preferable for any Y since it has the lower energy. One can conclude that in the model under consideration the symmetry breaking and fermion mass are generated dynamically by the boson self-interaction. The relationship between these results obtained within the renormalized formalism and the results of lattice calculations is analyzed. 14 refs., 10 figs