Abstract (Elsevier)
We show that there is a physical spacelike extra dimension of a circle (S 1 ) with small size β, the existence of fermions can cause dynamical instability of a vacuum at low energies 《 1/β by quantum effects. In a system consisting of gauge fields ( A μ ) and fermions with minimal gauge interactions an ordinary vacuum (〈 A μ 〉 = 0) is always destabilized by fermions obeying a periodic boundary condition in the extra dimensional coordinate. In a new vacuum the gauge symmetry remains unbroken, but fermions acquire dynamical masses by quantum corrections, even if they are massless at the tree level. We also present a toy model consisting of gauge and scalar fields in which SU(2) symmetry breaks down to U(1) without the scalar fields developing non-vanishing expectation value.