4 which (as we shall see in the next Section) have only small effects In our research on EWPT collisions, where we calculate the magnetic field produced by the EWPT, we need the equations for the Higgs and Stop fields, but in our present work on nucleation we only calculate the gauge fields, with the inlusion of the eletron current given in the following section. One of the most important features of the equa- tions of motion derived directly from the EW La- grangian is that the source current of the electromag- netic field is given by the charged gauge W ± fields, as seen from the Maxwell-like Eq.(14). This is ex- pected physically, and is in sharp contrast with the Kibble-Vilenkin[8], Ahonen-Enqvist[9], Copeland- Saffin-T¨ o rnkvist[10] picture. This suggests that we use an SU(2), isospin ansatz for the gauge fields. In the present paper we assume that with the I-spin operators defined as ϵ $^{mjk}$τ $^{j}$τ k = iτ $^{m}$. We shall see that this enables us to derive the straight-forward equations of motion for the electro- magnetic field, which can be solved to a good ap- proximation for symmetric nucleation of EW bub- bles. In this section we derive the e.o.m. for spheri- cally symmetric bubble nucleation, so that W ( x ) = W ( r, t ) and A ( x ) = A ( r, t ), with x $^{µ}$x$_{µ}$ = t 2 − r $^{2}$. First note that with F a function of W$_{ν}$ and ∂$_{ν}$W to be determined, so that the e.o.m. for W$_{ν}$ , Eq.(12), becomes In the present work we make use of the gauge fields gauge conditions to reduce the partial differential equations, Eqs(22,23), to ordinary differential equa- tions. The philosophy is to derive the W ± and A em fields as a function of r at a fixed time. Since from the general structure of the equations we expect at time t that the bubble wall will be at r = r$_{w}$ ≃ t , we are mainly interested in the nature of the fields near r = r$_{w}$ . As we shall see, since the solutions are modified instanton-like in nature, the most sig- nificant region for magnetic field creation for both nucleation, and for collisions, will be at the bubble walls. As pointed out at the beginning of this section, the current for the electromagnetic field arises en- tirely form the electrically charged fields/particles, W $^{±}$, as seen also in Eq.(23). Moreover, the cur- rent within our I-spin formulation is determined by a nonlinear partial equation for W ( r, t ), without direct coupling to the Higgs or Stop fields. This will enable us to derive the electromagnetic fields from EWPT bubble collisions as in Refs.[8–10]. In the present paper, however, we derive the electromagnetic fields produced in the EWPT via bubble nucleation before collisions, which has not been considered previously. For collisions a direction in space is singled out, so that the form W ( r, t ) , A ( r, t ) cannot be used. This is a topic for future work. Also, fermions contribute to the electric current, and fermion fields will be in- cluded in future work. The solution for A em pro- duced during nucleation with the assumptions of the present section are found in the following section. The most significant aspect of the I-spin formu- lation is that we obtain e.o.m. for W ( r, t ) and for A ( r, t ) without contributions from the Higgs or Stop fields. β = (+ , − ) for ν = ( t, j ). Subtracting the e.o.m. for W$_{t}$ × x$_{j}$ from the e.o.m. for W$_{j}$ × t we find III. I-SPIN ANSATZ AND ELECTROMAGNETIC FIELD CREATION FROM W ± A. I-Spin Ansatz W j ν ≃ iτ $^{j}$W$_{ν}$ ( x ) ≃ iτ $^{j}$x$_{ν}$ W ( x ) j = 1 , 2 , 3 A em ν ≃ iτ $^{3}$A$_{ν}$ ( x ) ≃ iτ $^{3}$x$_{ν}$ A ( x ) Z$_{ν}$ ≃ iτ $^{3}$Z ( x )$_{ν}$ ≃ iτ $^{3}$x$_{ν}$ Z ( x ) , (19) ( ∂ 2 t + ∂ 2 $_{r}$) W + t 2 + r 2 rt ∂$_{t}$∂$_{r}$W + ( 3 r ∂$_{r}$ + 3 t ∂$_{t}$ ) W + gW ( t 2 − r $^{2}$)( 1 t ∂$_{t}$ − 1 r ∂$_{r}$ ) W = 0 (22) ( ∂ 2 t + ∂ 2 $_{r}$) A + t 2 + r 2 rt ∂$_{t}$∂$_{r}$A + ( 3 r ∂$_{r}$ + 3 t ∂$_{t}$ ) A + GW ( t 2 − r $^{2}$)( 1 t ∂$_{t}$ − 1 r ∂$_{r}$ ) W = 0 . (23) ϵ $^{ijk}$Wjk ν = iτ i × F [ W$_{ν}$, ∂$_{ν}$W ] , (20) ∂ $^{µ}$∂$_{µ}$ W$_{ν}$ − ∂$_{ν}$∂$_{µ}$W µ − gx$_{ν}$ [5 W 2 + 3 W ( t∂$_{t}$ + r∂$_{r}$ ) W + gs $^{2}$W 3 − βs $^{2}$∂$_{r}$ W ] − g 2 2 ρ $^{2}$W$_{ν}$ = 0 , (21) with W$_{ν}$ = x$_{ν}$W ( r, t ) , s 2 = t 2 − r $^{2}$, r = √ ∑ 3 j =1 x $^{j}$xj = √ − ∑ 3 j =1 x $^{j}$x$_{j}$ , ∂$_{j}$r = x $^{j}$/r , and B. I-Spin Ansatz and Electromagnetic Field Creation During Nucleation Without Fermions