Self-energies for interacting fields with a compactified spatial dimension

We study the self-energy of a model with a tri-linear coupling among spinless fields on a manifold with one spatial dimension compactified. The model is considered to be composed by a quantized scalar field interacting with a classical scalar one. In order to improve the compactification we take the quantum field satisfying quasi periodic boundary conditions, which interpolates continuously the periodic and anti-periodic conditions, whilst the background field satisfies periodic boundary conditions. All the calculations are performed in Euclidean coordinates.

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