Timeline for How do we turn "Klein-Gordon space" into a Hilbert space?
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| S Nov 22 at 0:01 | history | bounty ended | WillG | ||
| S Nov 22 at 0:01 | history | notice removed | WillG | ||
| Nov 22 at 0:01 | vote | accept | WillG | ||
| Nov 14 at 7:46 | answer | added | flippiefanus | timeline score: 2 | |
| S Nov 14 at 5:42 | history | bounty started | WillG | ||
| S Nov 14 at 5:42 | history | notice added | WillG | Draw attention | |
| Nov 12 at 9:14 | comment | added | Tobias Fünke | Regarding your last comment: Yes, I agree, it is what I think but not explicitly checked (that was anyway not meant as a question, but more of a suggestion). But as it seems, I misunderstood your question. Regarding your actual question: It would be interesting to see what exactly Talagrand means here, i.e. what physicists write in certain QFT texts... but I don't know, it is not my field... | |
| Nov 12 at 7:30 | comment | added | WillG | @TobiasFünke Regarding your first question, $X_m$ has zero measure with respect to Lebesgue measure on $\mathbb R^{1,3}$, of which $X_m$ is a submanifold. Of course, $X_m$ has nonzero measure with respect to $d\lambda_m$. | |
| Nov 12 at 6:59 | comment | added | WillG | In other words, I want to make Talagrand's (mathematical) idea precise and answer his (mathematical) question—not his question about physicists' mental picture. | |
| Nov 12 at 6:56 | comment | added | WillG | @TobiasFünke No, I want the answer to the question Talagrand is asking (implicitly) in the sentence "my problem here is...". In other words, what is the norm on "that space," which makes the representation unitary? Note that "that space" is not $L^2(X_m, d\lambda_m)$, but rather some space $Y$ of functions satisfying the KG equation. To really answer Talagrand's question, you have to go further make precise what $Y$ even is. Moreover, I think $Y$ should be a Hilbert space and hence we really need an inner product on it, not just a norm. | |
| Nov 12 at 6:45 | comment | added | Tobias Fünke | Then I may misunderstand the question. Do you want to understand what Talagrand says about physicists? | |
| Nov 12 at 6:43 | comment | added | WillG | @TobiasFünke I don't doubt that $L^2(X_m, d\lambda_m)$ is well defined. My doubt is about the "space of functions on $\mathbb R^{1,3}$ whose Fourier transform is supported by $X_m$." | |
| Nov 12 at 6:40 | comment | added | Tobias Fünke | Regarding your last paragraph: I think $L^2(X_m,\mathrm d\lambda)$ is well-defined. Is $X_m$ a set of measure zero with respect to the given measure? | |
| Nov 12 at 5:32 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
added 4 characters in body; edited tags
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| Nov 12 at 5:04 | history | edited | WillG | CC BY-SA 4.0 |
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| Nov 12 at 4:20 | history | asked | WillG | CC BY-SA 4.0 |