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His statement (at about 6:08) is that one should treat only interacting bosons "if you want to have a non-pathological thermodynamic limit." The key is the phrase thermodynamic limit. In the thermodynamic limit, we take particle number $N\rightarrow \infty$ at constant density $N/V\rightarrow \text{const}$. It is this limit that is ill-defined for free ...

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Here is a Z decay to e+e- in lead lead collisions in CMS: The Z is "virtual" as we do not have fine grain enough detectors to see the vertex of e+e- as different in space than the event vertex, and thus know the distance the Z travelled. We know it is a Z because the mass of the summed fourvectors of the e+ e- gives the mass of the Z. So you see that the ...

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There is no extra mass going to virtual particles because they are not on mass shell. Read on. In this link a virtual photon is defined,second page, needed in calculating the crossection of electron electron scattering.(for low energies) The internal virtual lines are just a mnemonic in the integral that will give measurable quantities, a mnemonic with ...

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$\newcommand{\ket}[1]{\vert #1 \rangle}$ The issue is that $a^\dagger\ket{\phi} = \partial_\phi\ket\phi$ no longer is a coherent state. Hence $aa^{\dagger}\ket\phi \neq \phi\partial_\phi\ket\phi$ but rather $$aa^{\dagger}\ket\phi = \partial_\phi \phi\ket\phi$$ which looks totally counter-intuitive, but can be easily verified using the Taylor expansion. ...

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For block matrices we have the Helmert–Wolf formula  \left(\matrix{{\bf A}& {\bf B}\cr {\bf C}&{\bf D}}\right)^{-1} =\left(\matrix{({\bf A}^{-1}+{\bf A}^{-1}{\bf B}({\bf D}-{\bf C} {\bf A}^{-1}{\bf B}) {\bf C}{\bf A}^{-1} & -{\bf A}^{-1}{\bf B}({\bf D}-{\bf C}{\bf A}^{-1}{\bf B})^{-1} \cr -({\bf D}-{\bf C}{\bf A}^{-1}{\bf B})^{-1}{\bf C}{\bf A}^...

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