Timeline for Fourier and inverse fourier transform in QFT
Current License: CC BY-SA 3.0
10 events
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| Nov 27, 2014 at 6:08 | history | edited | Wen Chern | CC BY-SA 3.0 |
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| Nov 27, 2014 at 4:30 | comment | added | Rodrigo | Thank you for your answer! But can you explain how you got to the last line? I'm still a little confused about the difference between $\phi(p)$ and $\phi(\mathbf{p},t)$. The former (what's the word?) a particle with momentum $p$, the latter (...) a particle with momentum $\mathbf{p}$ at time $t$. But since a momentum $\mathbf{p}$ determines $p$ by $p=(E_{\mathbf p},\mathbf p)$, it seems that the latter is more "specific". Also, I think that you shouldn't have the square root in the factor $\frac 1 {2E_{\mathbf p}}$. | |
| Nov 27, 2014 at 3:33 | history | edited | Wen Chern | CC BY-SA 3.0 |
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| Nov 27, 2014 at 3:19 | history | edited | Wen Chern | CC BY-SA 3.0 |
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| Nov 27, 2014 at 3:14 | history | edited | Wen Chern | CC BY-SA 3.0 |
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| Nov 26, 2014 at 14:18 | comment | added | Wen Chern | Besides, the factor $\frac{1}{2E_{\mathbf{p}}}$ should be excluded from the first equation in your question. See, for instance, Peskin, An Introduction to Quantum Field Theory, p20. | |
| Nov 26, 2014 at 14:08 | comment | added | Wen Chern | I think it may be helpful to write the second equation in your original question in the form $\phi(\mathbf{p},t)=\int{d^3\mathbf{x}\phi(\mathbf{x},t)e^{-i\mathbf{p.x}}}$. Thus we see that $\phi(\mathbf{p},t)$ is not a function of $p$ with $p$ constrained by the mass shell condition, but a function of $\mathbf{p}$ and $t$. | |
| Nov 26, 2014 at 13:59 | comment | added | Wen Chern | Sorry, I misunderstood your question at the first time. | |
| Nov 26, 2014 at 13:12 | comment | added | Rodrigo | I understand 2., but can you elaborate on 1.? I think that one should start with an integral over the whole spacetime constrained by a delta function, like $\int d^4 x\delta(x_0)$ but I don't really see how the delta function $\delta(x_0)$ is analogous to $\delta(p^2-m^2)$ | |
| Nov 26, 2014 at 10:49 | history | answered | Wen Chern | CC BY-SA 3.0 |