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study of gravity wave production by magnetic fields created in the EWPT[24] 

In our present work A em ν ∼ x$_{ν}$A ( r, t ), so electric fields but no magnetic fields are created. This work can provide the initial conditions for EWPT colli- sions in which magnetic fields are created. 

## IV. ELECTROMAGNETIC FIELD CREATION DURING NUCLEATION WITH I-SPIN ANSATZ AND FERMIONS 

Let us now return to Eq(14), the e.o.m. for the em field with the electron current as well as the charged gauge fields 

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with the electron current at finite temperature[25] 

with ζ (3) ≃ 1 . 2, G= gg $^{′}$/ √ g 2 + g ′ $^{2}$=0.303, and u$_{e}$ a Dirac spinor. 

From Eq(14) we obtain the e.o.m. for A$_{r}$ ( t ) (see previous section) 

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with j = 0 . 028 M 3 $_{Higgs}$. We have taken T = M$_{Higgs}$ at the time of the EWPT. 

The solutions for A$_{r}$ ( t ) for fixed r are shown in Figs. 3 and 4. As one can see, the electron current plays an important role in electromagnetic field pro- duction during nucleation of EWPT bubbles. Note that the current of the charged W is approximately - jW$_{r}$ ( t ). The solutions for jW$_{r}$ ( t ) for fixed r, in comparison to the electron current, are shown in Fig 5. The function jWr ( t ) should be compared to the electron current = -0 . 084 r $^{2}$. Although the electron current is much smaller than the current from the W $^{+}$, W − fields near the bubble surface, the electron current is larger than the W $^{+}$, W − currents in the interior of the bubble.. 

Since the electron current is larger than the charged gauge currents inside the bubble, as shown in Fig. 5, we conclude that the leptonic currents must be included for the correct derivation of the magnetic fields during EWPT bubble collisions. 

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