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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.

"Mathematical physics consists of the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories." (from Journal of Mathematical Physics). This tag is intended for questions on mathematical methods used in quantum theory, general relativity, string theory, integrable system etc at an advanced undergraduate or graduate level.

Do not use just because your question involves physics!

See also Physics Stack Exchange's discussion on mathematical physics, Math Overflow's discussion on mathematical physics and Physics Overflow for further reference.

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Understanding the intermediate field method for the $\phi^4$ interaction

In Rivasseau's and Wang's How to Resum Feynman Graphs, on page 11 they illustrate the intermediate field method for the $\phi^4$ interaction and represent Feynman graphs as ribbon graphs. I had to read up about ribbon graphs as I've never heard of…
Huy
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Constructive weights to resum Feynman graphs

In Rivasseau's and Wang's "How to Resum Feynman Graphs", the weights of a spanning tree corresponding to a connected graph are defined as $$w(G,T) = \frac{N(G,T)}{|E|!},$$ where $N(G,T)$ is the number of Hepp sectors $\sigma = \{\sigma(1), \dots,…
user109923
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Optimization problem involving discrete and continuous variables

In my mechanics class I am to solve an optimization problem that is basically reduced to finding a set of points $x_i,y(x_i)$ such that the following functional is minimized: $$\sum\limits_{i}^{} \int_{f_1(x_{i-1},x_i)}^{f_2(x_i,x_{i+1})}…
I_am_ant
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How to correctly describe a set of joint level functions?

I have the Hamiltonian of some dynamical system: $$ H =\frac{p_1^2+p_2^2}{u(x_1)+v(x_2)}$$ Coordinates x=(x1, x2) change on the torus, therefore the functions u and v are 2pi-periodic. That is, the phase space is the cotangent bundle of a…
vkcomyo
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Is it possible to design a 4th dimensional circuit

I have a question related to higher dimensional topology and electrical engineering, It is incredibly common for engineers to come across schematics and diagrams for circuits which cannot exist in 2 dimensions but which can exist in 3 dimensions,…
Ethan
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Normalizing a function; Finding the solution to Burgers equation

I have been able to figure out the first half of the problem described below in the image. The part I am struggling on is finding the $C$ constant such that it will lead to a normalized solution of $\psi$. My understanding of normalizing a constant…
Battler
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What is the difference between normal and directional derivatives?

On pages 22 and 23 of H. K. Dass's Mathematical Physics, I read that both normal and directional derivatives are solved by finding the gradient of a surface and then putting a Cartesian value of a point on that surface in the the answer of gradient.…
Navjot Singh
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How to mathematically deal with unexpected negative value

For planck’s photon energy equation when calculating wavelength it makes no sense for it to be negative. The answer I get is negative because the energy value is the only negative variable, heat is given out so it’s said that the reaction is…
Nickotine
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Proof of the conservation law for the mass

I think I'm losing something while I'm trying to understand how to prove the conservation law for the mass. For example, Childress states (zipping passages at page 16): Let us suppose that mass is being added or subtracted from space as a function…
Gabrielek
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How can I solve these two equations to find theta?

I am doing a projectile motion questions and I have to solve these simultaneous equations: $$\frac{-5t^{2}+30t\sin\theta }{30t\cos\theta }=\frac{1}{\sqrt3}$$ $$\frac{-10t+30\sin\theta }{30\cos\theta }=-\sqrt3$$ I solved them but the solution is long…
please delete me
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A discrete torus with $L^d$ sides

I am taking a course in mathematical physics, and we've just begun a section in the lecture notes where we want to describe free electrons in the lattice $\mathbb{Z}^d$ for some $d$, which, to have physical meaning, is either $0,1,2$ or $3$. After a…
user478099
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Refractive index as a harmonic function of y

Given a refractive index of the form $n(y) = n_0 \cos(ky)$ , where $n_0$ and $k$ are positive constants. Is it possible to determine the trajectory of a ray of light, in the x-y plane, traveling through a medium with such a refractive index? through…
user134590
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Is the free Hamiltonian to the three body problem self-adjoint?

I have three particles: $x_0$ with mass $m$ and $x_1, x_2$ fermions with unitary mass. If I consider their free Hamiltonian I have $$H_0=-\frac{1}{2m}\Delta_{x_0}-\frac{1}{2}\Delta_{x_1}-\frac{1}{2}\Delta_{x_2}$$ acting on the space $$ \{f\in…
Fawkes
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Solution of the algebraic equation

I used to think about the following physics question. In quantum mechanics one has a quantity know as spin of a particle. A particle with total spin value $S$ (here $S\in\{0, 1/2, 1, 3/2, ...\}$ corresponds to an eigenvalue of the casimir operator…
Kiryl Pesotski
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Math identities, Poisson summation formula

I have derived this following formulas using Poisson summation formula. Can anyone kindly refer if this identity is derived or quoted somewhere? I wanted to be sure. \begin{equation} \sum_{n=0}^{\infty}e^{-\pi\left(n+\frac{1}{2}\right)^2 a…
lallu-bhoot
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