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What is the interpretation of Matsubara frequencies?

In QFT, the Matsubara frequencies are defined as $$\omega_n=\dfrac{2n\pi}{\hbar\beta}\quad\text{(bosons)}\quad\text{or}\quad\omega_n=\dfrac{(2n+1)\pi}{\hbar\beta}\quad\text{(fermions)},$$ where $\beta=...
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What is the meaning of thermal spectral function and thermal decay width in thermal field theory?

In Kallen-Lehmann spectral representation of 2-point correlation function \begin{equation} \langle 0|T\phi(x)\phi(0)|0\rangle=\int_0^\infty \frac{dM^2}{2\pi}\rho(M^2)D_F(x-y;M^2),\quad (a) \end{...