= Lorentzian quasiparticle spectral peak
{title2=$A(\mathbf k,\omega)=\Gamma_{\mathbf k}/[\pi((\omega-\Omega_{\mathbf k})^2+\Gamma_{\mathbf k}^2)]$}
A normalized retarded amplitude $G^R(\mathbf k,t)=-i\Theta(t)e^{-i\Omega_{\mathbf k}t-\Gamma_{\mathbf k}t}$, with constant $\Gamma_{\mathbf k}>0$, has <Fourier transform> $G^R(\mathbf k,\omega)=(\omega-\Omega_{\mathbf k}+i\Gamma_{\mathbf k})^{-1}$. Consequently $A=-\operatorname{Im}G^R/\pi$ is the displayed positive <Lorentzian line shape>, of unit frequency integral. Its maximum is at $\Omega_{\mathbf k}$ and its half width at half maximum is $\Gamma_{\mathbf k}$. The energy half-width is $\hbar\Gamma_{\mathbf k}$. Amplitude decays on time $1/\Gamma_{\mathbf k}$ whereas probability decays on time $1/(2\Gamma_{\mathbf k})$. A general interacting <Electron> has <quasiparticle residue> $Z$ and incoherent spectral weight in addition to this normalized local pole model; frequency-dependent width or <self-energy> can invalidate a global Lorentzian.
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