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Questions tagged [analyticity]

223 questions
60
votes
7 answers

Why does Taylor’s series “work”?

I am an undergraduate Physics student completing my first year shortly. The following question is based on the physical systems I’ve encountered so far. (We mostly did Newtonian mechanics.) In all of our analyses of the physical systems (up till…
Atom
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5 answers

Is the world $C^\infty$?

While it is quite common to use piecewise constant functions to describe reality, e.g. the optical properties of a layered system, or the Fermi–Dirac statistics at (the impossible to reach exactly) $T=0$, I wonder if in a fundamental theory such as…
Tobias Kienzler
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42
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3 answers

How can dimensional regularization "analytically continue" from a discrete set?

The procedure of dimensional regularization for UV-divergent integrals is generally described as first evaluating the integral in dimensions low enough for it to converge, then "analytically continuing" this result in the number of dimensions $d$. …
tparker
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36
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3 answers

What do the poles of a Green function mean, physically?

Is there a physical interpretation of the existence of poles for a Green function? In particular how can we interpret the fact that a pole is purely real or purely imaginary? It's a general question but I would be interested in the interpretation in…
PanAkry
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32
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Gaussian integral with imaginary coefficients and Wick rotation

Although this question is going to seem completely trivial to anyone with any exposure to path integrals, I'm looking to answer this precisely and haven't been able to find any materials after looking for about 40 minutes, which leads me to believe…
Adomas Baliuka
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27
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1 answer

Subtlety of analytic continuation - Euclidean / Minkowski path integral

I subconsciously feel not fully comfortable about Wick rotating or analytic continuation from Euclidean to Minkowski space. I simply wonder whether there is any subtlety here, and when we need to be conscious whether (i) this continuation can be…
wonderich
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27
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0 answers

Why does analytic continuation as a regularization work at all?

The question is about why analytical continuation as a regularization scheme works at all, and whether there are some physical justifications. However, as this is a relatively general question, I shall use the following examples to make the question…
user110373
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23
votes
5 answers

Why is analyticity a good mathematical assumption in general relativity?

In general relativity, real-variable analytic continuation is commonly used to understand spacetimes. For example, we use it to extend the Schwarzschild spacetime to the Kruskal spacetime, and also maximally extend the Kerr and Reissner-Nordstrom…
knzhou
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22
votes
1 answer

Derivation of KLT relations

The KLT relations (Kawai, Lewellen, Tye) relate a closed string amplitude to a product of open ones. While I get the physics behind this I don't really understand the derivation in the original paper (see https://doi.org/10.1016/0550-3213(86)90362-7…
A friendly helper
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19
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5 answers

Does the mass point move?

There is a question regarding basic physical understanding. Assume you have a mass point (or just a ball if you like) that is constrained on a line. You know that at $t=0$ its position is $0$, i.e., $x(t=0)=0$, same for its velocity, i.e.,…
Physicist
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19
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2 answers

How to understand "analytical continuation" in the context of instantons?

Since this is a subtle and interesting question to me. I will give a rather detailed description. I hope you can keep reading it and find it interesting too. For simplicity, in the following I will only discuss the one-dimensional instanton, that…
Wein Eld
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17
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2 answers

Feynman diagrams, can't Wick-rotate due to poles in first and third $p_0$ quadrants?

I have a confusion about relating general diagrams (involving multiple propagators) in Minkowski vs Euclidean signature, which presumably should be identical (up to terms which are explicitly involved in Wick-rotation). I'm confident the resolution…
Arturo don Juan
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What is the intuition behind Kramers-Kronig relations?

I have heard that Kramers-Kronig relations constrains the real and imaginary parts of complex permittivity $\varepsilon= \varepsilon^{'} + j\varepsilon^{''}$. What is the intuition behind this relation? Coming from an electrical engineering…
praveen kr
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15
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2 answers

Decoupling of Holomorphic and Anti-holomorphic parts in 2D CFT

This maybe a very naive question. I have just started studying CFT, and I am confused by why we have two separate parts of everything in CFT (operator algebras and hilbert space), the holomorphic and anti-holomorphic, which are decoupled from each…
user7757
14
votes
7 answers

Binary Black Hole Solution of General Relativity?

This is rather a technical question for experts in General Relativity. An accessible link would be an accepable answer, although any additional discussion is welcome. GR has well known solutions relating to single Black Holes: Schwarzchild, Rotating…
Roy Simpson
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