If you Lorentz transform a scalar:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]U^{-1}(\Lambda)\phi(x)U(\Lambda)=\phi(\Lambda^{-1}x) [/tex]

If you now perform another Lorentz transform, would it it look like this:

[tex]U^{-1}(\Lambda')U^{-1}(\Lambda)\phi(x)U(\Lambda)U(\Lambda')=\phi(\Lambda'^{-1}\Lambda^{-1}x) [/tex] ?

But isn't this wrong, because this expression is equal to:

[tex]U^{-1}(\Lambda\Lambda')\phi(x)U(\Lambda\Lambda')=\phi([\Lambda\Lambda']^{-1}x) [/tex]

and not:

[tex]U^{-1}(\Lambda'\Lambda)\phi(x)U(\Lambda'\Lambda)=\phi([\Lambda'\Lambda]^{-1}x) [/tex]

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# Lorentz transform of a scalar in QM

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