1. See, for example,E. W. Kolb andM. S. Turner:The Early Universe (Addison-Wesley, 1990) and references therein;A. Vilenkin:Phys. Rep.,121, 263 (1985).
2. A Minkowski metric is used with signature (+,−,−,−).
3. The overdot represents differentiation with respect tot.
4. TheU(1) gauge group need not be identified with the electromagnetic gauge groupU(1)EM.
5. If the phase cndition φ=Nϕ (N=integer) is chosen for eq. (10), then eqs (27) and (28) have right-hand sides multiplied byN, suggesting the presence of a gauge string containingN units of quantized flux.