Ej. Copeland et Pm. Saffin, BUBBLE COLLISIONS IN ABELIAN GAUGE-THEORIES AND THE GEODESIC RULE, Physical review. D. Particles and fields, 54(10), 1996, pp. 6088-6094
In an Abelian gauge symmetry, spontaneously broken at a first order ph
ase transition, we investigate the evolution of two and three bubbles
of the broken symmetry phase. The full field equations are evolved and
we concentrate, in particular, on gauge-invariant quantities, such as
the magnetic field and the integral around a closed loop of the phase
gradient. An intriguing feature emerges, namely, the geodesic rule, c
ommonly used in numerical simulations to determine the density of defe
cts formed, is shown not to hold in a number of circumstances. It appe
ars to be a function of the initial separation of the bubbles, and the
coupling strength of the gauge field. The reason for the breakdown is
that in the collision region the radial mode can be excited and it of
ten oscillates about its symmetry-restoring value rather than settling
to its broken symmetry value. This can lead to extra windings being i
nduced in these regions and, hence, extra defects (antidefects) being
formed.