= Solution
The <covariant derivative> $D_\mu$ differentiates a field while preserving its transformation law under the local <electroweak gauge symmetry> $SU(2)_L\times U(1)_Y$. Here $\partial_\mu$ is the ordinary spacetime derivative and $\mu$ a <Lorentz index>. The <gauge fields> $W^j_\mu$, $j=1,2,3$, are the three <SU(2)> fields; $B_\mu$ is the <U(1)> field. The corresponding dimensionless <coupling constant (physics)> is $g$ for <SU(2)> and $g'$ for <U(1)>.
The $\tau_j$ are <weak isospin> generators in the representation of the differentiated field, with $\tau_j=\sigma_j/2$ on a doublet and $\tau_j=0$ on an <SU(2)> singlet. The repeated index $j$ is summed. The generator $Y/2$ supplies the field's <weak hypercharge> in the convention $Q=\tau_3+Y/2$, where $Q$ is its fractional <electric charge>. The factor $-i$ follows the convention of Hermitian generators. The two connection terms compensate the derivatives of spacetime-dependent <gauge transformations>.
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