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Dec
3
comment Operator-state correspondence in QFT
I'm not saying that we never do things like this in physics, but that it isn't exactly what is meant by "local" (at least to me). For example, in the standard Penrose diagram for Minkowski space, past timelike infinity is mapped to a single point, but if you want to talk about local processes occurring in a neighborhood of that point you really have to blow it up to resolve that. There's also a technical issue as to in what sense the limits converge. On AdS this would be a whole different story of course, but in flat space it doesn't make much sense to regard past infinity as a single point.
Dec
3
comment Operator-state correspondence in QFT
@Axion I agree with Prahar's comment. Perhaps another way to say this is that in a CFT, 0 is literally a point, in that we can compute correlation functions between fields at 0 and other points. In an ordinary QFT, past infinity isn't such a thing. The idea of contracting past infinity to a single point seems inherently nonlocal, in that if I send two wave packets back in time in opposite directions in flat space, I expect them to be getting farther away from each other, not converging to the same point...
Dec
2
answered Operator-state correspondence in QFT
Sep
25
comment How to deal with the notation of a function $f$ vs its value $f(x)$ in Physics?
Are you familiar with the implicit function theorem? Many of the "functions" you describe are probably better understood by mathematicians as relations, which can be converted locally into functions via this if you need to do so.
Sep
25
awarded  Popular Question
Sep
22
comment How deep can my knowledge of particle physics go without the maths?
"Physics, by definition, is the subset of Mathematics which pertains to our universe." I disagree with this. There's plenty more to physics than just pure math. I tend to agree more with Vladimir Arnold that the containment is in the other direction: "Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap."
Sep
18
answered Does Clifford algebra depend on the topology of manifold?
Sep
17
awarded  Fanatic
Sep
9
answered Why is the value of thrust for a perfectly spherical event equal to ${\frac{1}{2}}$?
Sep
8
comment What are the physical dimensions (units) of the elements in a Hilbert space of a QM system?
@REX Thanks for catching that. I've now corrected it. I make silly typos like that all the time.
Sep
8
revised What are the physical dimensions (units) of the elements in a Hilbert space of a QM system?
fixed another minor error
Sep
8
revised What are the physical dimensions (units) of the elements in a Hilbert space of a QM system?
fix silly error
Sep
8
answered What are the physical dimensions (units) of the elements in a Hilbert space of a QM system?
Aug
26
awarded  Talkative
Aug
4
awarded  Popular Question
Jul
12
awarded  Yearling
Jul
11
answered Direct Sum of Hilbert spaces
Jul
9
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Jun
14
awarded  Critic
May
7
asked What exactly is meant by the conformal group of Minkowski space?