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In Chapter 7 of Terning's book (Modern Supersymmetry), the first example considered is that of an $SO(3)$ gauge theory, a complex scalar in the triplet representation of $SO(3)$ and a potential term:

$$\mathcal{L} = \int d^{4}x \left[-\frac{1}{4}F^{a}_{\mu\nu}F^{a,\mu\nu} + (D_\mu\phi^a)^* (D^\mu\phi^a) - \frac{\lambda}{4}(\phi^{a*}\phi^a - v^2)^2\right]$$

The author says

The energy of a static field configuration in the Prasad-Sommerfield (PS) limit $\lambda \rightarrow 0$ is

$$E = \frac{1}{2}\int d^{3}x \left[B_i^a B^{ai} + (D_i\phi^a)^*(D^i\phi^a)\right]$$

Why is there no kinetic term of the form $E_i^a E^{ai}$ corresponding to the Yang-Mills electric field?

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Because the static solution considered is the 't Hooft and Polyakov monopole. There is no (non-Abelian) electric field in this case. A more general solution would be a dyon and then the electric field contributes to the mass of the particle.

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