Timeline for Explicit Form of Feynman Propagator for a Scalar Field in Position-space: Derivation Details
Current License: CC BY-SA 4.0
13 events
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| Dec 12, 2023 at 1:10 | comment | added | naturallyInconsistent | Yes and yes. You should just consult a good textbook on tensors as used in physics to understand the argument better, though. | |
| Dec 11, 2023 at 16:13 | comment | added | agfdsa | @naturallyInconsistent Would you be able to elaborate at all on your last sentence? Do you refer to the equal treatment of spacetime coordinates, sort of like space- and time-like coordinates are treated equivalently in the KG equation (at least in terms of order of derivatives) in contrast to the Schrodinger equation? So then you enforce identical dependence in the time-coordinate when now taking $\Delta t \neq 0$ as you have just derived in the spatial coordinates? | |
| Dec 11, 2023 at 16:06 | comment | added | agfdsa | Thank you @mb28025 for the resources; they look very helpful. | |
| Dec 8, 2023 at 5:58 | comment | added | naturallyInconsistent | A lot of mathematical facts are simply noticing of relations. For example, the integral representation of special functions might simply be taken as their definitions, and then shown to solve the differential equations, etc. Or some other equally tenuous path. There seems to be a sign mistake in the quoted solutions when promoting to Lorentz invariance. As for why promotion works, you have to convince yourself when you study tensors that specific functional form dependences is a thing. | |
| Dec 7, 2023 at 20:52 | comment | added | mb28025 | As far as your second question goes, try this. It really goes through all the steps and explicitly states many details that are usually assumed the reader is aware of. | |
| Dec 7, 2023 at 20:20 | comment | added | mb28025 | As far as your first question is concerned, there are a lot of sources online about limiting behavior of special functions. Indeed $K_1 (z) \sim 1/z$ for small $z$ and therefore $mK_1(mr)\rightarrow 1/r$ for $m\rightarrow 0$. I think that recalling that the $+i\varepsilon$ prescription is just a regulator will also clear up any confusion on why is the denominator $4\pi^2 r^2 +i\varepsilon$ and not $4\pi^2 r^2 +i\varepsilon r$. | |
| Dec 7, 2023 at 19:56 | review | Close votes | |||
| Dec 23, 2023 at 3:03 | |||||
| Dec 7, 2023 at 19:38 | history | edited | Voulkos |
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| Dec 7, 2023 at 18:06 | history | edited | agfdsa | CC BY-SA 4.0 |
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| Dec 7, 2023 at 17:58 | history | edited | agfdsa | CC BY-SA 4.0 |
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| Dec 7, 2023 at 17:06 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
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| S Dec 7, 2023 at 16:36 | review | First questions | |||
| Dec 7, 2023 at 17:35 | |||||
| S Dec 7, 2023 at 16:36 | history | asked | agfdsa | CC BY-SA 4.0 |