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Questions tagged [physics]

For questions about mathematical problems arising from physics, the natural science studying general properties of matter, radiation and energy.

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Approximate solutions to $x''(t)=-cx + f(t)x$

I recently studied a problem which involved two particles joined by a harmonic spring moving in a potential and through some manipulation, I obtained the equation $x''(t) = -\omega^2x + f(t)x$, where $...
FusRoDah's user avatar
  • 3,738
6 votes
0 answers
371 views

What is the predictive power of each object in QFT, and how are they related? [closed]

My background is not in physics or mathematical physics, so this question is mostly out of ignorance, and probably easily known to experts. Basic Setup You begin with a spacetime $M$. (Minkowski in ...
Tim Phalange's user avatar
1 vote
0 answers
65 views

Some details about relationship between central charges and second cohomology group of the Lie algebra

S. Weinberg in his book "The quantum theory of fields" talks about central charge that appear in Lie algebra of a given Lie group. To be more precise, on page 83 in the book, he computes the ...
Mahtab's user avatar
  • 287
1 vote
0 answers
205 views

Are causally isomorphic spacetimes Wick-related?

Take the time-orientable spacetimes $(M_1,g_1)$ and $(M_2,g_2)$ that are locally(to be clarified below) Wick-related and both are globally Wick-rotatable(to be clarified below) to the same Riemannian ...
Bastam Tajik's user avatar
1 vote
0 answers
228 views

Is the topological dimension of spacetime fixed for causally isomorphic spacetimes?

Suppose time-oriented spacetimes $(M_1 , g_1)$ and $(M_2, g_2)$ are not homeomorphic under their manifold topologies $\mathcal{M}_1$ and $\mathcal{M}_2$ respectively. The Lorentzian metrics $g_1$ and $...
Bastam Tajik's user avatar
1 vote
0 answers
170 views

Order isomorphism + manifold homeomorphism => path topology homeomorphism?

Suppose time-oriented spacetimes $(M_1 , g_1)$ and $(M_2, g_2)$ are homeomorphic under their manifold topologies $\mathcal{M}_1$ and $\mathcal{M}_2$ respectively. Let's call this map $\phi: (M_1, \...
Bastam Tajik's user avatar
1 vote
1 answer
361 views

Can the Causal Structure recover the manifold topology for non-chronological spacetimes?

Given a time-oriented spacetime $(M,g)$, a binary relation $\ll$ can be defined on this spacetime where $p \ll q$ for $p, q \in M$ if and only if there exists a time-like path connecting $p$ and $q$. ...
Bastam Tajik's user avatar
11 votes
2 answers
2k views

Why/does 'low-dimension' topology end with dimension 4? [duplicate]

Put another way, assuming it is somewhat fair to say that we (not I, but those who know better--part of my question is whether my stated assumption is in fact warranted) have in some sense a ...
Troubled Shallows's user avatar
0 votes
0 answers
100 views

I'm looking for the NLab page on particle species

This is just a reference request. I came across an NLab page on particle species described as certain vector bundles. But I can't seem to find it again when I searched recently. If someone can point ...
Mozibur Ullah's user avatar
14 votes
1 answer
1k views

Hilbert's sixth problem and QFT description

The Wikipedia entry on Hilbert's sixth problem about QFT description is “Since the 1960s, following the work of Arthur Wightman and Rudolf Haag, modern quantum field theory can also be considered ...
XL _At_Here_There's user avatar
32 votes
8 answers
4k views

Motivation and physical interpretation of the Laplace transform

Concerning the one-sided Laplace transform, $$\mathcal{L}\{f\}(s) = \int_0^\infty f(t)e^{-st} dt$$ what is a motivation to come up with that formula? I am particularly interested in "physical&...
AlpinistKitten's user avatar
-2 votes
1 answer
141 views

Interpretation and validity of modified Heisenberg uncertainty principle in a metric context? [closed]

Considering the Heisenberg uncertainty principle, which states $\Delta x \cdot \Delta p \geq h$, I've explored a modified version by computing $(\Delta x + 1)(\Delta p + 1) \geq \Delta x \cdot \Delta ...
mathoverflowUser's user avatar
1 vote
1 answer
213 views

Qualitative values between two electrons in an atom or how to interpret these values?

This question is a little bit trying to understand physics through geometry of simplex: Let $E_{i,j}$ be the ionization energy in times the number of hydrogen ionization energy for an element with ...
mathoverflowUser's user avatar
0 votes
1 answer
663 views

What is this three dimensional curve that looks like an infinity sign called?

What is this three dimensional curve that looks like an infinity sign called? (Is there a known parametric equation for it?) It was generated with this Sagemath - script, where you can zoom in 3d in ...
mathoverflowUser's user avatar
1 vote
1 answer
294 views

Temporal evolution of a globally hyperbolic spacetime

Any globally hyperbolic spacetime can be assigned a global function of time as Hawking has demonstrated for stably causal spacetime. (Any globally hyperbolic spacetime is also stably causal). For ...
Bastam Tajik's user avatar
0 votes
1 answer
746 views

A RKHS interpretation of the Rydberg formula for hydrogen and an application for physics?

I was thinking if it is possible to define an inner product between two small physical objects with a positive definite kernel and was led to look at the Rydberg formula: The Rydberg formula for ...
mathoverflowUser's user avatar
1 vote
0 answers
80 views

Biot-Savart-like integral for a toroidal helix

The following problem originates from Physics, so I apologize if I will not use a rigorous mathematical jargon. Let us consider a toroidal helix parametrized as follows: $$ x=(R+r\cos(n\phi))\cos(\phi)...
AndreaPaco's user avatar
1 vote
1 answer
119 views

calculating a double limit

We have the following term: $$ (e^{-a h}+e^{-b h})^n / 2^n$$ Now we take the limit: $$ h\to 0, n\to \infty $$ What relation of $h$ and $n$ must be satisfied for the following limit to hold? $$\lim_{h\...
Lili Si's user avatar
  • 105
3 votes
1 answer
249 views

Interesting question about the Thomson problem for arbitrary number of electrons

This question is crossposted from here I believe this is a pretty hard question and so I decided to repost the question in the Math Overflow forum. If there is something wrong with doing this, I am ...
Rodrigo's user avatar
  • 51
3 votes
1 answer
146 views

Applications of maximal surfaces in Lorentz spaces

I have been working on minimal surfaces, only recently learnt about maximal surfaces and "maxfaces" in Lorentz spaces. I can clearly see the mathematical motivations. But I wonder if zero-...
Hao Chen's user avatar
  • 2,581
-4 votes
2 answers
530 views

Inverse square-law as a positive definite kernel?

Newtons law for gravity states that: $$F_{12} = \frac{G m_1 m_2} {|x_1-x_2|^2}$$ The function : $$k(x,y):=\exp(-| x-y|^2)$$ is known to be a positive definite function, called the RBF-kernel. It ...
mathoverflowUser's user avatar
3 votes
1 answer
244 views

inclusion of von Neumann algebras implies reversing inequality of its modular operators

I'm working with von Neumann algebras and I stumbled with this statement in a work of Borchers (1999) Since $\mathcal N \subseteq \mathcal M$, it follows by standard arguments that $\Delta_{\mathcal ...
Gabriel Palau's user avatar
3 votes
1 answer
579 views

Mathematical difference between solitons and traveling waves for a non-linear dispersive PDE

I see many mathematicians conflating the definitions of traveling waves and solitons, and I am unable to understand, from a mathematical point of view, the differences between these two types of ...
Niser's user avatar
  • 73
1 vote
0 answers
93 views

How to smoothly interpolate gravitational field between trajectories in high dimension?

I'm looking for the adequate numerical interpolation technique to solve the following problem. This is probably trivial for physicists who study gravitational fields, but I didn't find clear answers ...
Youcef's user avatar
  • 19
10 votes
1 answer
566 views

D'Alembert's Principle: rigorous formulation using notions from modern differential geometry

Is there a rigorous definition of D'Alembert's principle of virtual dynamic work in the language of differential geometry? Some questions I'm hoping to answer are: How to view the configuration space ...
mcmathy's user avatar
  • 101
1 vote
0 answers
142 views

A question about Roger Penrose's spin networks and mathematical formalization?

Let $a,b,c$ be "units" in the spin network. Then there are there are the following three requirements to fulfill (according to the relevant Wikipedia entry): $a,b,c \in \mathbb{N}$ Triangle ...
mathoverflowUser's user avatar
1 vote
0 answers
183 views

polynomial approximation of hypergeometric function 2F1

I have the following function $T(k_1,k_2)$ resulting from multiphoton transition matrix elements calculations: $T(k_1,k_2)=\gamma^{-k_2}\sum_{j=0}^{k_1}(j+2)_{l+1}\binom{k_1}{j}(k_1+1)_3(\gamma-1)^{j}{...
Omer Amit's user avatar
0 votes
1 answer
282 views

Mathematical characterization of gravitational geons as reference request, and their properties as main question

I've edited (ten days ago) a question on Physics Stack Exchange, this Mathematical characterization of gravitational geons, post with identifier 726281 the users of the site were kind adding in the ...
user142929's user avatar
5 votes
0 answers
126 views

Particles sent into the same direction with uniformly distributed speed

Fix a positive integer $n$. Every second, a particle is sent along a straight line from a fixed position in a fixed direction, at a random integer speed chosen uniformly in $\{1,\ldots, n\}$ meters ...
Dominic van der Zypen's user avatar
19 votes
9 answers
6k views

How does a Masters student of math learn physics by self?

I am a Masters student of math interested in physics. When I was an undergraduate, I took the introductory course of physics, but it is just slightly harder than high school physics course. To be ...
LZB's user avatar
  • 193
2 votes
1 answer
371 views

Examples of ODEs with complex constant coefficients and applications to physics?

This question is asked on stackexchange: Are there examples for ODEs with complex coefficients with applications in physics? but received no answers. I am reposting it here on the hope that it catches ...
Medo's user avatar
  • 852
3 votes
0 answers
214 views

How to calculate the integral of a product of a spherical Hankel function with associated Legendre polynomials

From numerical experiments in Mathematica, I have found the following expression for the integral: $$ \int_{-1}^{1}h_{n}^{(1)}\left(\sqrt{a^{2}+b^{2}+2ab\tau}\right)P_{n}^{m}\left(\frac{a\tau+b}{\sqrt{...
Chris's user avatar
  • 31
9 votes
1 answer
385 views

Why are discreteness and smoothness in physics inversed with respect to geometry?

In a closed (say differentiable) Riemannian manifold you see only continuous features when looking at small neighbourhoods of points. From afar, discrete features appear ((co)homology, closed ...
Roland Bacher's user avatar
3 votes
0 answers
108 views

Are square configurations the only critical points of the energy on the circle?

$\newcommand{\S}{\mathbb{S}^1}$ $\newcommand{\la}{\lambda}$Let$$M=\{(x_1,x_2,x_3,x_4) \in (\S)^4\,\, |\,\, \text{ all the } x_i \, \text{ are distinct}\} $$ Define $E:M \to \mathbb{R}$ by $$E(x_1,x_2,...
Asaf Shachar's user avatar
  • 6,741
4 votes
0 answers
116 views

Superspace derivation of supersymmetric non-linear sigma model in Supersolutions by Deligne and Freed

I am having a little trouble understanding passage from the linear to the non-linear sigma model in Section 4.1 of Supersolutions by Deligne and Freed. Most of my confusion comes down to the ...
user avatar
4 votes
1 answer
706 views

Why are solenoidal fields called solenoidal?

A solenoidal tangent field, mathematically speaking, is one whose divergence vanishes. They are also called incompressible. I understand why they are called incompressible — a fluid flow is called ...
Mozibur Ullah's user avatar
16 votes
1 answer
753 views

From a physicist: How do I show certain superelliptic curves are also hyperelliptic?

As the title suggests, I am a physicist and have a question about how to show certain superelliptic curves are also hyperelliptic. The superelliptic Riemann surfaces in question has the form $$w^n = \...
Kestrel's user avatar
  • 163
19 votes
4 answers
2k views

Applications of complex exponential

In calculus we learn about many applications of real exponentials like $e^x$ for bacteria growth, radioactive decay, compound interest, etc. These are very simple and direct applications. My question ...
Max's user avatar
  • 199
4 votes
1 answer
403 views

How are spatial coordinate systems in physics defined?

Grothendieck once asked "What is a meter?" (https://golem.ph.utexas.edu/category/2006/08/letter_from_grothendieck.html). This innocent sounding question, made me to think about how ...
mathoverflowUser's user avatar
2 votes
0 answers
171 views

Is there an example Hamiltonian that is uncomputable?

In a paper from 2015 Toby S. Cubitt et al showed that the problem of determining the existence of a band gap in the excitation spectrum of a quantum many-body system, was undecidable. This result ...
user400188's user avatar
2 votes
4 answers
336 views

EM-wave equation in matter from Lagrangian

Note I am not sure if this post is of relevance for this platform, but I already asked the question in Physics Stack Exchange and in Mathematics Stack Exchange without success. Setup Let's suppose a ...
Chopin's user avatar
  • 61
-1 votes
1 answer
437 views

Harmonic function in infinite domain in $\mathbb{R}^3$, constant on the boundary and decaying as $1/r^2$

EDIT: Let $\Omega\subset \mathbb{R}^3$ be a bounded domain with smooth connected boundary. Let $f\colon \mathbb{R}^3\backslash \Omega \to \mathbb{R}$ be a continuous function which is harmonic in $\...
asv's user avatar
  • 21.8k
0 votes
1 answer
468 views

Harmonic functions in infinite domain in Euclidean space

EDIT: Let $\Omega\subset \mathbb{R}^n$ be a bounded domain with smooth boundary. Let $f\colon \mathbb{R}^n\backslash \Omega \to \mathbb{R}$ be a continuous function which is harmonic in $\mathbb{R}^n\...
asv's user avatar
  • 21.8k
0 votes
0 answers
99 views

The specific connection between the Hecke operator and the t'Hooft Operator

As I was reading some articles concern about the Selberg trace formula and its general form, I have noticed that the Selberg trace formula and its general form can be understand as the energy spectrum ...
loveimissyou123's user avatar
2 votes
1 answer
164 views

Vacuum state generating functional

In Theorem 1 of this paper Segal stablish a relation between states and generating functionals. He assert that in order to $\mu$ be a generating functional must satisfy $$ \sum_{j,k\in F} \mu (z_j-...
Gabriel Palau's user avatar
8 votes
0 answers
1k views

Is there any physics theory which is similar to these analogies?

Since I am doing this little "research" project on my spare time and in my physical neighborhood there are not many people to discuss these ideas, I wanted to share with you a small point of ...
mathoverflowUser's user avatar
11 votes
1 answer
1k views

State of rigorous effective quantum field theories

It's well-known that there are no rigorously constructed and physically relevant QFTs. There is, however, a lot of mathematical work on effective field theories and renormalization, such as the books ...
Pedro's user avatar
  • 279
4 votes
1 answer
670 views

Formula involving Wigner's 3j symbols and integration over irreducible representations of SU(2)

$\DeclareMathOperator\SU{SU}$In some calculations, I saw the following formula $$\int_{\SU(2)}\,\mathrm{d}g\,D^{j_{1}}_{m_{1}n_{1}}(g)D^{j_{2}}_{m_{2}n_{2}}(g)D^{j_{3}}_{m_{3}n_{3}}(g)=(-1)^{j_{1}+j_{...
B.Hueber's user avatar
  • 1,171
4 votes
2 answers
2k views

Reference for mathematical Palatini formalism of general relativity

I know that this is maybe not a research level question, but since the topic is quite special, I thought that the chance to get some reference is higher in this community. I am looking for a reference ...
B.Hueber's user avatar
  • 1,171
1 vote
0 answers
192 views

Angular velocity from rotation matrix difference [closed]

I am working on something for a game. I need to calculate the angular velocity, however in my situation I only have access to the previous rotation matrix and the current rotation matrix. My angular ...
Chryfi's user avatar
  • 111