Abstract
We look at the ground state, or vacuum, solutions for self-interacting scalar fields confined in cavities where the boundary conditions can rule out constant field configurations, other than the zero field. If the zero field is unstable, symmetry breaking can occur to a non-constant field configuration that has a lower energy. The stability of the zero field is determined by the size of the length scales that characterize the cavity and parameters that enter the scalar field potential. There can be a critical length at which an instability of the zero field sets in. In addition to looking at the rectangular and spherical cavity in detail, we describe a general method which can be used to find approximate analytical solutions when the length scales of the cavity are close to the critical value.
Published Version
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