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Can anybody help me with the proof that [itex] E_p \delta ({\bf p}- {\bf q}) [/itex] is a Lorentz invariant object?

I did a boost along z axes and used the formula [tex] \delta (f(x)) = \frac{\delta(x-x_0)}{|f'(x_0)|} [/tex] and the factor in front of the delta function indeed is invariant but within the function I have something like this:

[tex] E_p \delta (p_z -(v(E_q-E_p)+q_z)) [/tex]

but not [itex] E_p \delta (p_z- q_z)[/itex]

Thanks.

I did a boost along z axes and used the formula [tex] \delta (f(x)) = \frac{\delta(x-x_0)}{|f'(x_0)|} [/tex] and the factor in front of the delta function indeed is invariant but within the function I have something like this:

[tex] E_p \delta (p_z -(v(E_q-E_p)+q_z)) [/tex]

but not [itex] E_p \delta (p_z- q_z)[/itex]

Thanks.

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