4-FERMION INTERACTION-MODEL ON R(2)XS(1) - A DYNAMICAL DIMENSIONAL REDUCTION

A four-fermion interaction model is studied on R2 X S1 spacetime. The fermion is supposed to acquire a phase e(i2pidelta) (0 less-than-or-equal-to delta less-than-or-equal-to ) along a circulation of the circle S1 whose circumference is L. We evaluate the effective potential to the leading order of the 1/N expansion. It is shown that for 1/6 < delta < 5/6 there is a critical circumference L(c) which is analytically found. The chiral symmetry breaking occurs only for L < L(c). The lowest vacuum energy density (the minimum of effective potential) for delta and L is shown at delta = 0 and L --> 0, which may be a kind of dynamical dimensional reduction.