The phase structure of a four-fermion theory is investigated in compact flat spaces as a simple model of dynamical symmetry breaking, motivated by recent studies on similar considerations in curved space. A useful formalism is developed to evaluate the effective potential in arbitrary compact flat spaces in three- and four-dimensional spacetimes. It is found that the phase structure is significantly altered due to the finite-size effect in the compact space. This finite-size effect exhibits different features depending on the boundary conditions on the fermion fields. When antiperiodic boundary conditions are imposed, the dynamical symmetry tends to be restored due to the finite-size effect. Contrastingly, it tends to be broken, when periodic boundary conditions are imposed.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy (miscellaneous)