# Questions tagged [mathematical-physics]

DO NOT USE THIS TAG for elementary physical questions. This tag is intended for questions on modern mathematical methods used in quantum theory, general relativity, string theory, integrable system etc at an advanced undergraduate or graduate level.

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### Hawking and Ellis's example of an extendible manifold

In S. Hawking's and G. Ellis's book "The Large-Scale Structure of Space Time", they discuss the notion of inextendible Lorentz manifolds $(M,g)$ (see chapter 3.1). A Lorentz manifold is ...
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### Self-dual $126$ and $126^*$ in SO(10) or Spin(10) Irreps

We are looking at 126 or $126^*$ in SO(10) or Spin(10) Irreps. 126 is known as a complex total "anti-symmetric" and "self-dual" 5-index tensor irreps in Spin(10). This means the ...
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### What's the difference between $v = a\cdot t$ and $\vec{v} = \int \vec{a} \, \mathrm dt$

In highschool, I learned $v = at$ and in university, I am learning $\vec{v} = \int \frac{\vec{F}}{m} \, \mathrm dt = \int \vec{a} \, \mathrm dt$. I understand one is for $v= at$ is for one-dimension ...
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### Proof for First Null Point in Boresight

I was doing some of the exercises of a textbook about radars and encountered this exercise from the problem section (without answer); check question link or the Question: Two antennas are D distance ...
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### Domain issues in transformation of the coordinate representation of a function

Start with a Manifold $M$ and define a function $f:M\rightarrow\mathbb{R}$. As usual, pick two charts $(U,x)$ and $(V,y)$ with $p \in U\cap V$ and $x:M \supset U \rightarrow x(U) \subset\mathbb{R}^n$. ...
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### Finding the radius of curvature of the trajectory of a projectile.

The parabolic trajectory of a projectile has different radius of curvature at different points of time. Is there a way to find R of C for a simple projectile, thrown at an angle θ and initial ...
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### Galiliean group vs Poincare group and role of mass

In what follows I'm trying to generalize an approach from Landau & Lifschits Vol 1 -- unfortunately, the authors use it only in Vol 1 discussing Newtonian mechanics. I was trying to apply the same ...
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### On Green function of $\nabla^2u(\vec{r})=\rho(\vec{r})= \delta\,(\vec{r}-\vec{r}_1)-\delta\,(\vec{r}-\vec{r}_2)$ in the semiplane $x > 0$ [closed]

Could someone please help me with this problem? I'm not good with math and that problem seems very challenging to me. Using the Green function, solve the following problem in the semiplane $x > 0$:...
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### Constant invariant quantities

What is the intuition behid the constant invariant quantities and why do we need it? How is this related with probability theory? I was solving some maximization problem and when I saw the answer, the ...
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### Who are the current leading researchers in the field of symmetry analysis of differential equations applied to physics? [closed]

I want to study symmetry analysis of differential equations to find exact solutions. I have heard of Ibragimov, Bluman, Hydon and Olver from textbooks. I would like to know which researchers are ...
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### Normalization Eigenvector [closed]

Could you find for pic attachement Thank you
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### Coin tossing experiment : A geometric approach

A coin is tossed at random. We assume that the thickness of the coin is $0$ and in rotation,the vector of the normal applied to the heads side of the coin generates a cone.The axis of the cone makes ...
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### the Holographic Principle

https://mathoverflow.net/questions/365765/this-is-topology-solved?noredirect=1#comment923604_365765 Assume extreme competence. The holographic principle, as described below in this question, is ...
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### Ferris wheel Trig Question [duplicate]

Question: Suppose you wanted to model a Ferris wheel using a sine function that took 60 seconds to complete one revolution. The Ferris wheel must start 0.5 m above ground. Provide an equation of such ...
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### Laplacian coupled with another equation over a two-dimensional rectangular region

I have the two-dimensional Laplacian $(\nabla^2 T(x,y)=0)$ coupled with another equation. The Laplacian is defined over $x\in[0,L], y\in[0,l]$. On manipulating the second equation (which I have ...
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### A ferris wheel completes 2 revolutions in 30 seconds. Determine how far it has travelled in 15 seconds. The radius of the ferris wheel is 10 m. [closed]

If the Ferris wheel completes two revolutions in $30$ seconds, how many revolutions does the Ferris wheel complete in $15$ seconds? The radius of the Ferris wheel is 10 m. I'm stuck in this question, ...
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### LHS where the argument of the function isn't explicit stated (vector equation)

The Lorentz force is given as $$\mathbf F= q\left[\mathbf E(\mathbf r(t),t)+\mathbf v(t)\times \mathbf B(\mathbf r(t),t)\right] \tag 1$$ where $\mathbf E, \mathbf B:\mathbb R^4\to\mathbb R^3$ are ...
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### When finding the position function $s=f(t)$ from $v(t)$ at $f(0)=0$, why are the bounds of integration $0$ to $t$? [closed]

It comes from this question. A particle moves on a straight line with velocity function $v(t) = \sin \omega t \cos ^2\omega t$. Find its position function $s= f(t)$ if $f(0) = 0$. Thank you!
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### Factorization method for solving differential equations

I want to solve the second order differential equation as follows $\gamma\xi\left(1-\xi x^2\right)W''+\left(-\xi x^2+\beta\gamma\xi^2x+1\right)W'+\beta x\xi W=0$. My suggestion is the factorized ...
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### Finding a class $C$ of bipartite PPT states such that entanglement of $\rho \in C$ implies entanglement of $\rho + \rho^{\Gamma}$.

Consider an entangled bipartite quantum state $\rho \in \mathcal{M}_d(\mathbb{C}) \otimes \mathcal{M}_{d'}(\mathbb{C})$ which is positive under partial transposition, i.e., $\rho^\Gamma \geq 0$. As ...
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### How are spin network edges related to anti-symmetric projectors on the Hilbert space of the fundamental rep of SU(2)?

In the paper here https://arxiv.org/pdf/gr-qc/9905020.pdf we see an introduction to Spin-networks of the original Penrose type i.e an undirected open graph whose edges have labels that are irreducible ...