# Tagged Questions

"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 methods used ...

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### What are BesselJ functions?

I solved an integration on mathematica which gives BesselJ functions and some other terms. I explored mathematica help and google but could not understand the difference between different types of ...
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### Why do zeta regularization and path integrals agree on functional determinants?

When looking up the functional determinant on Wikipedia, a reader is treated to two possible definitions of the functional determinant, and their agreement is trivial in finite dimensions. The first ...
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### Is $\nabla$ a vector?

The following passage has been extracted from the book "Mathematical methods for Physicists": A key idea of the present chapter is that a quantity that is properly called a vector must have the ...
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### Regularity of an infinite series arising with the heat equation

Let $(t,y)\in(0,\infty)\times\mathbf{R}$, and $\displaystyle f(t,y) \equiv \sum_{k=-\infty}^{\infty}\frac{\exp(-(y-2\pi k)^2/2t)}{\sqrt{2\pi t}}$. This infinite series arises if one attempts to solve ...
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### What's the Clifford algebra?

I'm reading a book on Clifford algebra for physicists. I don't quite understand it conceptually even if I can do most algebraic manipulations. Can some-one teach me what the Clifford algebra really is?...
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### Area enclosed by an equipotential curve for an electric dipole on the plane

I am currently teaching Physics in an Italian junior high school. Today, while talking about the electric dipole generated by two equal charges in the plane, I was wondering about the following ...
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### Arnold's theorem on action-angles.

I changed the question slightly in its form to make it more readable. I have a question about the action-angle theorem on p. 283 in Arnold's textbook on classical mechanics.(I added the link to this ...
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### In what ways has physics spurred the invention of new mathematical tools?

I came across this comment: Mathematical rigor is not a criterion that physicists have for evaluating their theories. From a mathematical perspective, the non-rigorous theories are far more ...
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### Is there any abstract theory of electrical networks?

Designing electrical networks is among the highly mathematical engineering disciplines, which uses a vast scope of techniques from Fourier analysis and complex function theory, to logic, combinatorics ...
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### Correct spaces for quantum mechanics

The general formulation of quantum mechanics is done by describing quantum mechanical states by vectors $|\psi_t(x)\rangle$ in some Hilbert space $\mathcal{H}$ and describes their time evolution by ...
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### Mathematically rigorous text on classical electrodynamics.

Is there any textbook (preferably not written by a physicist) on classical electrodynamics which gives a rigorous (by the standards of pure mathematics) treatment of (a part of) the topics found in ...
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### Gathering books on Lorentzian Geometry

I find it very hard to find books on Lorentzian Geometry, more focused on the geometry behind it, instead of books that go for the physics and General Relativity approach. More specifically, I'm ...
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### Gentle introduction to fibre bundles and gauge connections

To better understand papers like this for example, which makes heavy use of fibre bundles and gauge connections to represent gauge fields, I am looking for a nice introduction to this topic. The only ...
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### Evaluate the Integral using Contour Integration (Theorem of Residues)

$$J(a,b)=\int_{0}^{\infty }\frac{\sin(b x)}{\sinh(a x)} dx$$ This integral is difficult because contour integrals normally cannot be solved with a sin(x) term in the numerator because of ...
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### Guide to mathematical physics?

I am currently a math phd student specializing in algebraic geometry aspiring to work at the boundaries of the the fields of mathematics and physics and so, was looking into the field of mathematical ...
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### Existence and uniqueness of Stokes flow

What are the solution existence and uniqueness conditions for Stokes' flow? $$\begin{gathered} \nabla p = \mu \Delta \vec{u} + \vec{f} \\ \nabla \cdot \vec{u} = 0 \end{gathered}$$ Maybe you could ...
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### What are spinors mathematically?

In the wikipedia article on spinors a number of mathematical definitions are given of spinors which I find slightly confusing. There are essentially two frameworks for viewing the notion of a ...
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### How to get the asymptotic form of this oscilatting integral?

So the integral is like this: $$\int_1^\infty \frac{\cos xt}{(x^2-1)\left[\left(\ln\left|\frac{1-x}{1+x}\right|\right)^2+\pi^2\right]}\mathrm{d}x$$ The question is how to get the asymptotic form of ...
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### Green's function in a moving frame for a constant heat source

I am looking for the Green's function of the problem in two dimensions $r =(x,z)$, $$\nabla^2g + \frac{v}{D}\frac{\partial g}{\partial z} = -\delta (r-r_0)$$ Which ...
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### What went wrong? [One-dimensional-inverse-square-law]

Intrigued by this question, one-dimensional inverse square laws, I started to try to find an answer and came up with what follows. However, I calculated the derivatives to double check myself, and ...
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### Universal Covering Group of $SO(1,3)^{\uparrow}$

I'm trying to prove that $SL(2,\mathbb{C})$ is the universal covering group for the proper orthochronous Lorentz group $SO(1,3)^{\uparrow}$. The standard way goes as follows. (1) Exhibit a real ...
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### Momentum a cotangent vector?

Imagine we have a particle described by $x \in M$, where $M$ is some manifold, then it is very intuitive I think that a velocity is an element of the tangent space at $x$, so $x' \in T_{x}M.$ Thus, by ...
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### Spinor Mapping is Surjective

I'm (still) trying to prove that $SL(2,\mathbb{C})$ is the universal covering group the the proper orthochronous Lorentz group $L$. I have completed the following steps. (1) Prove that the vector ...
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### What are elements in $SU(1, 1)$?

I am reading some papers in physics. I don't know some notations in those papers. For example, $SU(1, 1)$, $U(1)$. I think these are Lie groups which consist of matrices. But I don't know what kind of ...
Let $d\in\left\{2,3\right\}$ and $\Omega_t$ be the bounded set occupied by a fluid at time $t\ge 0$. Let $c\in\Omega_0$ be a particle and [0,\infty)\to\mathbb R^d\;,\;\;\;t\mapsto X_t(c)\in\Omega_t\...