Again, I am having difficulty deciphering my class notes - in this case there are missing lines of explanation. If we consider a system of particles that approach and interact, the Heisenberg representation of the interacting field is:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\phi(\vec{x} , t) = U^{-1} (t) \phi_{a} (\vec{x} , t) U(t)[/tex]

(where [tex]\phi_a[/tex] is the free field before the interaction.

Why is it that we can write:

[tex]\frac{\partial}{\partial t} \phi_{a}= \frac{\partial}{\partial t} U \phi U^{-1}=[\frac{\partial}{\partial t} UU^{-1},\phi_{a}]+iU[H,\phi]U^{-1} [/tex]

where the square brackets in the third equality are commutators?

I don't understand where the third expression comes from?

Thanks.

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# Pertubation Theory

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