# Questions tagged [mathematical-physics]

DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com. Mathematical physics is the mathematically rigorous study of the foundations of physics, and the application of advanced mathematical methods to problems in physics. Examples include partial differential equations (PDEs), variational calculus, functional analysis, and potential theory.

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### How are coefficients of equation of sideslip angle in the paper “A general Solution to the Aircraft Trim Problem” calculated?

I am sure many of you guys(Aerospace related) must have read the paper, "A General solution to the Aircraft Trim Problem" by Marco, Duke and Bernt. I am working with the turning of the Aircraft and I ...
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### What is a NS-2 brane?

This is a question about topological string theory. The existence of a new brane called "an NS-2 brane" is predicted in (the second paragraph in the page 14 of) the paper N=2 strings and the ...
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### Line integral of a point charge

I am trying to teach myself Electrodynamics through self-study of Griffiths' Introduction to Electrodynamics, and I am having difficulty with a calculation that involves a line integral of a point ...
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### Expression for sum over paths

In an introductory lecture on the path integral formalism, I came across the following. Suppose that $\gamma$'s are paths such that a particle travelling along any of them reaches the position co-...
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### What are infinitesimal formally? [duplicate]

Can any problem in physics involving infinitesimal be converted to a rigorous epsilon Delta argument? Say for example finding the moment of inertia of a continuous body? Another is what is the ...
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### Can a null hypersurface be foliated by spacelike sections?

Let $(M,g)$ be a $d$-dimensional Lorentzian manifold and let $\Sigma \subset M$ be a null hypersurface, which therefore has dimension $(d-1)$. We know that its normal vector $k^\mu$ is null and since ...
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### Index on a compact manifold

How can the integral of a topological term (like the Nieh-Yan term) on all of a compact manifold be nonzero whereas it's a total derivative and the manifold has no boundary? I assume the manifold can ...
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### Meaning of Kronecker Product in Partially Expanded Operators

I am studying operators in quantum mechanics and have reached confusion in the meaning of the Kronecker product of such operators. I am fairly lost so please excuse any errors in the following text. ...
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### Discussion: Mathematically precise physical textbooks [closed]

I am very interested in the abstract mathematical description of nature. Therefore, I have recently started to compile a list of good textbooks about physics, which have a very high level of ...
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### Measure-theoretic force

I understand classical mechanics as a science of moving masses. So I decided to work out it formulation based on measure there just for fun. In this framework the classical mechanical system would be ...
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### How to prove that $u(r)=k \dfrac{1}{r}$ is the only solution for the integral equation $\displaystyle\int_{V'}\rho'\ u(r)\ dV' = constant$?

Consider a hollow spherical charge with density $\rho'$ continuously varying only with respect to distance from the center $O$. $V'=$ yellow volume $k \in \mathbb {R}$ $\forall$ point $P$ inside ...
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### Why is integral of product of a test function and derivative of Dirac-delta function seems to diverge? [closed]

Suppose,we have to evaluate the integral $\int_{-\infty}^{\infty}f(x)\delta'(x)dx$ Traditionally to solve this,we integrate by parts so that the integral is equal to$-f'(0)$,which is finite if $0$ is ...
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### Measuring phase constants from the sine function

In simple harmonic motion, is the phase, by definition, always measured using the sine function? I'm asking because a question came up that provided $\omega$ and the amplitude, and also specified the ...
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### How to calculate the total gravitational potential energy of a vertical object (do we use integration?)

Hello I was reading another question asked by zach466920, and when he was trying to calculate the total GPE of a water 'tower', he used this explanation: He basically used integration to calculate ...
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### Relation between Scattering Matrix and Correlation matrix

Scattering matrix is the matrix which transform an input vector to an output vector. On the other hand Correlation matrix is the matrix of auto-correlation and cross correlation functions. Where we ...
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### Does the concept of infinity have any relevancy or application in Physics and applied Physics? [duplicate]

Does the concept of infinity have any relevancy or application in Physics and applied Physics? I must admit that I am not particularly knowledgeable in the area of Physics, but I have never seen the ...
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### Past boundary of $\mathcal{I}^+$ and future boundary of the hyperboloid resolving $i^0$

Let us consider Minkowski spacetime. Let $(u,r,x^A)$ be retarded coordinates with $x^A$ coordinates on the sphere. Future null infinity is described here as the $r\to \infty$ limit with $(u,x^A)$ ...
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### Calculation of one-point functions in causal perturbation theory

How are one-point functions evaluated in causal perturbation theory? I'm not sure where my mistake is in following the standard procedure. Take the first-order coupling $T_1=\lambda \phi^3$. Within ...
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### Can the real-time Green's function be written in the form of path integral on the real axis? [closed]

In every textbook, the path integral of the Green's function is written in imaginary-time. I wonder whether we could write real-time green function in the path integral form.
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### Mathematical understanding of band energy

Let me first give a sketch of how I understand band energy mathematically. It is not exactly rigorous, but probably could be made rigorous under suitable conditions. Let $H$ denote the Hamiltonian on ...
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### What is the advantage of using Kruskal coordinates?

(as opposed to Eddington-Finkelstein coordinates) The EF coordinates already take care of the coordinate singularity so I dont see a point for using Kruskal coordinates.
Let me start with the definitions I'm used to. Let $I[\Phi^i]$ be the action for some collection of fields. A variation of the fields about the field configuration $\Phi^i_0(x)$ is a one-parameter ...