Spectral methods compute the one-loop vacuum polarization energy for kink and sine-Gordon domain walls in up to 3+1 dimensions, matching exact results in 1+1 and 2+1 and giving analytic results at arbitrary renormalization scale.
The on-shell-residue (OSR) scheme augments the OS conditions by requiring that the residue of the propagator does not have any quantum correction
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Quantum contribution to domain wall tension from spectral methods
Spectral methods compute the one-loop vacuum polarization energy for kink and sine-Gordon domain walls in up to 3+1 dimensions, matching exact results in 1+1 and 2+1 and giving analytic results at arbitrary renormalization scale.