We investigate the effects of the homogeneous Neumann boundary conditions in the scalar electrodynamics with self-interaction. We show that if the length of the finite region is small enough ([Formula: see text], where Mϕ is the mass of the scalar field generated by the Coleman–Weinberg mechanism) the spontaneous symmetry breaking will not be induced and the vector field will not develop mass, however the scalar field will.
In this work we show that homogeneous Neumann boundary conditions inhibit the Coleman-Weinberg mechanism for spontaneous symmetry breaking in the scalar electrodynamics if the length of the finite region is small enough (a = e 2 M −1 φ , where M φ is the mass of the scalar field generated by the Coleman-Weinberg mechanism).
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