電子光子相互作用
H ^ ′′ = e 2 m e ∑ k , ν = 1 , 2 ∑ k ′ , ν ′ = 1 , 2 π ħ ω k ω k ′ V 2 ε ν ( k ) ⋅ ε ν ′ ( k ′ ) ( a ^ k ν + a ^ − k ν † ) ( a ^ k ′ ν ′ + a ^ − k ′ ν ′ † ) e i ( k + k ′ ) ⋅ r {\displaystyle {\hat {H}}''={\frac {e^{2}}{m_{e}}}\sum _{\mathbf {k} ,\nu =1,2}\sum _{\mathbf {k'} ,\nu '=1,2}{\frac {\pi \hbar }{\sqrt {\omega _{\mathbf {k} }\omega _{\mathbf {k'} }V^{2}}}}{\boldsymbol {\varepsilon }}_{\nu }(\mathbf {k} )\cdot {\boldsymbol {\varepsilon }}_{\nu }'(\mathbf {k'} )({\hat {a}}_{\mathbf {k} \nu }+{\hat {a}}_{-\mathbf {k} \nu }^{\dagger })({\hat {a}}_{\mathbf {k'} \nu '}+{\hat {a}}_{-\mathbf {k'} \nu '}^{\dagger })e^{i(\mathbf {k+k'} )\cdot \mathbf {r} }}
である。