Ms. Volkov, COMPUTATION OF THE WINDING NUMBER DIFFUSION RATE DUE TO THE COSMOLOGICAL SPHALERON, Physical review. D. Particles and fields, 54(8), 1996, pp. 5014-5030
A detailed quantitative analysis of the transition process mediated by
a sphaleron-type non-Abelian gauge field configuration in a static Ei
nstein universe is carried out. By examining spectra of the fluctuatio
n operators and applying the zeta-junction regularization scheme, a cl
osed analytical expression for the transition rate at the one-loop lev
el is derived. This is a unique example of an exact solution for a sph
aleron model in 3 + 1 spacetime dimensions.