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4momentum in relativistic QM 
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#1
Jun3008, 03:37 AM

P: 2,954

I've been wondering about relativistic quantum mechanics. Elsewhere I'm addressing some comments about this branch of physics but I have never studied it. Is the 4momentum 4vector defined in the same way in relativsitic QM or is there a difference? I'm wondering if the time component of 4momentum is defined in the same way in relativistic QM as in classical relativity. Thanks.
Pete 


#2
Jun3008, 03:57 AM

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P: 1,135

In QFT the 4momentum is typically associated with the phase change rates in the time and space components corresponding to the plane wave eigenfunctions: [tex]\psi(x)~=~e^{iEt/\hbar + ipx/\hbar}[/tex] Regards, Hans 


#3
Jun3008, 03:59 AM

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PF Gold
P: 9,414

It's defined as the [itex]P^\mu[/itex] that appears in the translation operator [itex]e^{iP^\mu a_\mu}[/itex], where [itex]a^\mu[/itex] is the translation fourvector. This definition works in both relativistic and nonrelativistic QM. (The best place to read about these things is chapter 2 of vol. 1 of Weinberg's QFT book).
In a relativistic quantum field theory, you can also construct the fourmomentum operators expliclity from the Lagrangian, as the conserved quantities that Noether's theorem tells us must exist due to the invariance of the action under translations in space and time. 


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