The Anti-Ferromagnetic Vacuum

Certain effective vertices may generate a non-homogeneous, periodic vacuum structure. The excitations above such a vacuum are studied in the framework of the ${\varphi }^4$ and gauge models. The formation of the non-homogeneous vacuum is accompanied by the dynamical breakdown of the space-time inversion symmetry. Chiral transformation is introduced for bosons in close analogy with lattice fermions.