Neumann Boundary Conditions Inhibiting SSB in Coleman—Weinberg Mechanism

Abstract

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).

Quantum Yang-Mills field theory

“…Otherwise, the mechanism cannot be granted to generate mass as pointed out both for the case of the scalar field [21,22] and ColemanWeinberg mechanism [23,24]. About confinement, it should be emphasized that it is the combination of Yukawa-like propagators, showing mass gap, and a running coupling to possibly yield a confining potential [25,26,27].…”