I am reading through sidney colemans lectures on QFT and I am stuck on what seem to be a silly question: He talks about the fact that the measure used in a calculation should be invariant in order to prove unitarity and later on that operators transform properly. He uses the example of rotational invariance.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]U^{-1}(R)\int d^{3}k|k><k| U(R)[/tex]

[tex]\int d^{3}k |R^{-1}k><R^{-1}k|[/tex]

Change of variable: Rk' = k

Now this is the part I dont get (I must be confused)

[tex]d^{3}k' = d^{3}k[/tex]

It seems to me like there should be a factor of R or something. However, the strange thing is that R is a matrix (isn't it?) so I dont really get it. Can someone explain what is going on here?

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# Invariant measures

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