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We quantise from first principles field theories living on the background of
a bubble wall in the planar limit with particular focus on the case of
spontaneous breaking of gauge symmetry. Using these tools, we compute the
average momentum transfer from transition radiation: the soft emission of
radiation by an energetic particle passing across the wall, with a particular
focus on the longitudinal polarisation of vectors. We find these to be
comparable to transverse polarisations in symmetry-breaking transitions with
mild super-cooling, and dominant in broken to broken transitions with thin
wall. Our results have phenomenological applications for the expansion of
bubbles during first order phase transitions. Our general framework allows for
the calculation of any particle processes of interest in such translation
breaking backgrounds.
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