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

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Here a marginally trapped surface is a spacelike surface in a 4-dimensional Lorentzian manifold such that the mean curvature vector field is everywhere lightlike. Is it absurd from a physical point of ...
Louis's user avatar
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I'm reading a paper under the title Ghost channels and ghost cycles guiding long transients in dynamical systems, here or here. The authors state that by examining simple ordinary differential ...
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Suppose real-valued wave function $\psi(r_1,\dots,r_N)\in L^2$ (or $H^1$) is unnormalized and antisymmetric, that is: $$\psi(r_{\sigma(1)},\dots,r_{\sigma(N)}) = \text{sgn}(\sigma)\psi(r_1,\dots,r_N),\...
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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
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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
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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
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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 ...
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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
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Suppose the 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
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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
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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 ...
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Concerning the one-sided Laplace transform, $$\mathcal{L}\{f\}(s) = \int_0^\infty f(t)e^{-st} dt$$ what is a motivation to come up with that formula? I am particularly interested in "physical&...
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Considering the Heisenberg uncertainty principle, which states $\Delta x \cdot \Delta p \geq h$, I've explored a modified version by computing $(\Delta x + 1)(\Delta p + 1) \geq \Delta x \cdot \Delta ...
mathoverflowUser's user avatar
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This question is a little bit trying to understand physics through geometry of simplex: Let $E_{i,j}$ be the ionization energy in times the number of hydrogen ionization energy for an element with ...
mathoverflowUser's user avatar
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What is this three dimensional curve that looks like an infinity sign called? (Is there a known parametric equation for it?) It was generated with this Sagemath - script, where you can zoom in 3d in ...
mathoverflowUser's user avatar
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Any globally hyperbolic spacetime can be assigned a global function of time as Hawking has demonstrated for stably causal spacetime. (Any globally hyperbolic spacetime is also stably causal). For ...
Bastam Tajik's user avatar
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I was thinking if it is possible to define an inner product between two small physical objects with a positive definite kernel and was led to look at the Rydberg formula: The Rydberg formula for ...
mathoverflowUser's user avatar
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The following problem originates from Physics, so I apologize if I will not use a rigorous mathematical jargon. Let us consider a toroidal helix parametrized as follows: $$ x=(R+r\cos(n\phi))\cos(\phi)...
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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? $$\lim_{h\...
Lili Si's user avatar
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This question is crossposted from here I believe this is a pretty hard question and so I decided to repost the question in the Math Overflow forum. If there is something wrong with doing this, I am ...
Rodrigo's user avatar
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I have been working on minimal surfaces, only recently learnt about maximal surfaces and "maxfaces" in Lorentz spaces. I can clearly see the mathematical motivations. But I wonder if zero-...
Hao Chen's user avatar
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Newtons law for gravity states that: $$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
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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 ...
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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
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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 ...
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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
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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
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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
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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
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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 ...
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23 votes
12 answers
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I am a Masters student of math interested in physics. When I was an undergraduate, I took the introductory course of physics, but I noted it was slightly harder than a high school physics course. To ...
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LZB
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1 answer
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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 ...
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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
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9 votes
1 answer
450 views

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
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$\newcommand{\S}{\mathbb{S}^1}$ $\newcommand{\la}{\lambda}$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,...
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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
987 views

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
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16 votes
1 answer
820 views

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
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19 votes
4 answers
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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
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1 answer
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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
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2 votes
4 answers
452 views

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
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-1 votes
1 answer
501 views

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
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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
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0 votes
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138 views

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
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2 votes
1 answer
195 views

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 $$ \sum_{j,k\in F} \mu (z_j-...
Gabriel Palau's user avatar
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Since I am doing this little "research" project on my spare time and in my physical neighborhood there are not many people to discuss these ideas, I wanted to share with you a small point of ...
mathoverflowUser's user avatar
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11 votes
1 answer
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It's well-known that there are no rigorously constructed and physically relevant QFTs. There is, however, a lot of mathematical work on effective field theories and renormalization, such as the books ...
Pedro's user avatar
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4 votes
1 answer
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$\DeclareMathOperator\SU{SU}$In some calculations, I saw the following formula $$\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_{...
user avatar
4 votes
2 answers
2k views

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 ...
user avatar
1 vote
0 answers
215 views

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 ...
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