- #1
ananya J
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QFT Peskin p.30 eqn 2.54
i am perplexed with eqn 2.54 peskins introductory qft. just can't make out how to arrive at it from the previous step. i think that there are dirac delta funtions involved but simply can't make it out. can somebody help? provide some hint? thanks in advance for ur time
3. The Attempt at a Solution
[tex]\int\ \frac{d^3p} {(2\pi)^3}\ \{ \frac {1}{2E_p}\ e^{-ip.(x-y)}\left|_{p^0 = E_p}\ +\ \frac {1}{-2E_p}\ e^{-ip.(x-y)}\left|_{p^0 = -E_p}\ \}= \int\ \frac{d^3p} {(2\pi)^3}\ \int\ \frac{dp^0} {2p^0}\ e^{-ip.(x-y)}\ \{ \delta (p_0-E_p) +\delta (p_0+E_p)\ \}[/tex] [tex]= \int\ \frac{d^3p} {(2\pi)^3}\ \int\ dp^0\ e^{-ip.(x-y)}\ \delta(p^2-m^2)[/tex]
dont know if iam on the right track.pls correct me if am wrong.
Homework Statement
i am perplexed with eqn 2.54 peskins introductory qft. just can't make out how to arrive at it from the previous step. i think that there are dirac delta funtions involved but simply can't make it out. can somebody help? provide some hint? thanks in advance for ur time
3. The Attempt at a Solution
[tex]\int\ \frac{d^3p} {(2\pi)^3}\ \{ \frac {1}{2E_p}\ e^{-ip.(x-y)}\left|_{p^0 = E_p}\ +\ \frac {1}{-2E_p}\ e^{-ip.(x-y)}\left|_{p^0 = -E_p}\ \}= \int\ \frac{d^3p} {(2\pi)^3}\ \int\ \frac{dp^0} {2p^0}\ e^{-ip.(x-y)}\ \{ \delta (p_0-E_p) +\delta (p_0+E_p)\ \}[/tex] [tex]= \int\ \frac{d^3p} {(2\pi)^3}\ \int\ dp^0\ e^{-ip.(x-y)}\ \delta(p^2-m^2)[/tex]
dont know if iam on the right track.pls correct me if am wrong.
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