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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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Looking for a translation

Reading the book "Fundamentals of Renewable Energy Processes I came across an equation I am not sure how to read. The equation is: $$J_0=q\frac{4\pi}{h^3}mk^2T^2exp(-\frac{q\phi}{kT}) $$ I am looking at this and I am not sure how to read this. Is…
Chris
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What do the equations on this gate mean or relate to?

These equations are on gates to the John Dalton building in Manchester UK: $$X \geq Y \text{ iff } \not\exists \, x_r \leq Y \text{ & } X \leq Y_L $$ $$X = Y \text{ iff } X \leq Y \text{ & } Y \geq X$$ Here’s a picture of the gates Does anybody…
minimum
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show $\sum_{i=1}^\infty a_i^{\ast}b_i$ is convergent using the Schwarz inequality

Question: Let $\{a_i\}_{i=1}^\infty$ and $\{b_i\}_{i=1}^\infty$ be in $\mathbb{C}^\infty$. Show $\sum_{i=1}^\infty a_i^{\ast}b_i$ is convergent, using in particular the Schwarz inequality. Attempt at answer: $\{a_i\}_{i=1}^\infty$,…
Desperate Fluffy
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Lie-Trotter Decomposition and Leapfrog Method Splitting Method

I'm not sure I can ask this question, if it causes some problem, then I would immediately delete the post. I'm looking at "Spinsim" Package, and at the guide pdf, it shows some math technique: I'm not so good in mathematics, and I have just found…
user21091084
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Help understanding the result obtained in a paper concerning renormalization group

I am reading the paper Large financial crashes and I noticed that it uses the renormalization group (RG) formalism. Here are some excerpts from the paper: It continues by writing that we notice that the solution (3) of the RG equation (2) together…
Mark
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System of equations with sin and cos being multiplied?

If $V_1,V_2$ are known, how would I solve this system of equations: $$\begin{cases} V_1 = \dfrac{\sin(x)\sin(y)}{\cos(x)} \\V_2 = \dfrac{\cos(x)}{\sin(x) \cdot \cos(y)} \end{cases}$$ The final result should be in degrees or radians it doesn't…
Frank
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Component free calculation of poisson brackets

How can the Poisson bracket {H, A} be computed directly without components. H is the Hamiltonian for the inverse square force, H=p^2/m- k/|r| , and A is the integration constant called the Laplace vactor; A = pxrxp/m-mkr/|r| At first glance the…
Gauge
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Liouville integrability

I am trying to understand how to use Liouville integrability to solve a question, but I could not understand how to calculate the functions $H_1,\ldots,H_n$ which are functionally independent (their wedge product is not equal to zero) and…
Maria
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Calculate distance travelled by particle with positive velocity and negative acceleration in fixed time

Let's assume a ball is thrown upwards with an initial velocity V and gravitational acceleration -A is acting on it in downward direction At some height H the particle with reach its max height and start falling down in negative direction I want to…
Omkar T
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Using Euler-Lagrange equation for a purely kinetic lagrangian

Suppose in a system of $n$ dynamic degrees of freedom $q_i$, $i=1,\dots,n$, there is only kinetic energy: $$L=\frac{1}{2}\sum_{a,b}g_{ab}(q_i)\dot{q_a}\dot{q_b}$$ where $g_{ab}(q_i)=g_{ba}(q_i)$ are the components of a symmetric $n\times n$ matrix.…
End points
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Is it true that two 3D bodies of different shapes cannot have the same volume to area ratio unless both have exactly the same volume and area?

I found this elegant physics question in the Q/A section of the research gate. My own judgment is that this is true except, and only except, for complete spherical shapes. . In other words, it applies well to both hemispheres and to all shapes other…
user1122527
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Math puzzle not that hard but i cant find what am i missing

The braking distance for a truck with the speed measured in km/h is $\frac{v^2} {100}$ meters, the “reaction distance” (distance driven during the reaction time) is about $\frac v 4$. For save driving, the distance between one truck driving behind…
Creedance
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Force between loops

It is physics (force between loops) but the highlighted term is equal to zero and I don't understand it. It is from Stokes' theorem but I don't understand it.
Mary Dona
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How many turns are needed to get a length L of the steel blade roll?

I'm doing a college project and I came across the need to calculate how many turns it takes to get a length $L$ of a steel blade roll. I am not able to develop a formula for this. The roll length formula I'm using is:$$L=\frac{\pi}{T}\cdot \left…
Luan Henrique
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Derivation of the shape of the catenary curve, clarification of a particular step

I find the derivation of the shape of the catenary curve by Jeremy Tatum in the libretexts version of his book quite elegant. I reuse an image from an earler catenary question: Tatum defines: $\mu$ mass per unit of length of chain $g$ gravitational…
Cleonis
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