Questions tagged [physics]
For questions about mathematical problems arising from physics, the natural science studying general properties of matter, radiation and energy.
194 questions
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Bosonic String Theory
I would like clarification of 26 dimensional Bosonic String Theory. A definition would be, that this is free bosons compactified on a torus and orbifolded by a 2-point reflection group (or ...
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1
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697
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Which motion is exclusive in 3D or higher dimensions?
Hi guys,
I have a simple question
Linear movement can be found in 1D, 2D and 3D world objects
Rotation can be found in 2D and 3D world objects.
Now, are there any kind of motion can only be found ...
- 101
3
votes
2
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3k
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Something like mathoverflow in other sciences [closed]
Are the sites similar to mathoverflow in other sciences related to mathematics? statistics, computer science, physics, economics, etc?
Let me explain what I mean by "similar": those are sites devoted ...
3
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4
answers
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Applications of Hamiltonian formalism to classical mechanics
In many courses in theoretical classical mechanics Hamiltonian formalism takes an important place. However I did not see it applied to problems of classical mechanics (unless one expands the scope of ...
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2
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Maxwell Stress Tensor and Equations in Mathematician's Language [closed]
In my language, a differential two-form on $\mathbb{R}^4$ (viewed as a differentiable manifold with coordinates $t,x,y,z$) is a differentiable choice at each point of an alternating bilinear function ...
- 15.4k
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Does current follow the path(s) of least (total) resistance?
Consider Poisson equation $\nabla \cdot (\sigma(x)\nabla u)=0$ in a domain $D$, where $\sigma(x)$ is the spatially dependent conductivity. On the boundary we have $2$ electrodes $E_1$ and $E_2$ (...
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3
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2
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434
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Classification of Lagrangians with given Euler-Lagrange equations
In (mathematical) physics the equations of motion of a system of particles are often interpreted as Euler-Lagrange equations for appropriate Lagrangian $L=L(x,\dot x,t)$ where $x$ is a collection of ...
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3
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Legendre equation: An interpretation [closed]
I am a student of physics and, especially in quantum mechanics, we are presented with the Legendre equation:
\begin{eqnarray}
(1-x^2)y''-2xy'+l(l+1)y=0.
\end{eqnarray}
Doing some calculations, we ...
3
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1
answer
579
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Mathematical difference between solitons and traveling waves for a non-linear dispersive PDE
I see many mathematicians conflating the definitions of traveling waves and solitons, and I am unable to understand, from a mathematical point of view, the differences between these two types of ...
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2
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Translation of an article
I need to read this article
"On the spectrum of an energy operator for atoms with fixed nuclei in subspaces corresponding to irriducible representations of permutation groups"
authors:G.Zhislin, A. ...
- 73
3
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1
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Applications of maximal surfaces in Lorentz spaces
I have been working on minimal surfaces, only recently learnt about maximal surfaces and "maxfaces" in Lorentz spaces.
I can clearly see the mathematical motivations. But I wonder if zero-...
- 2,581
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wave speed and travelling wave
I have seen a lot of work has been done in the context of travelling wave. For example the work of McKenna and Chen in Journal of Differential Equations Volume 136, Issue 2, 20 May 1997, Pages 325-355....
- 402
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512
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Wave front set of vector-valued Dirac delta distribution
Context: I am reading a physics paper Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime which applies the notion of the wave front set to operator-valued ...
- 193
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1
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Boundary conditions for Klein-Gordon equation
Let us consider the Klein-Gordon equation
$$(\Box +m^2)u=0,$$
where $u$ is a scalar valued function, $m\geq 0$, $\Box=\frac{\partial^2}{\partial x_0^2}-\sum_{i=1}^d\frac{\partial^2}{\partial x_i^2}$.
...
- 21.8k
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Conserved quantities for the Cauchy momentum equation
I apologize if this question is too elementary for mathoverflow; I asked it (unsuccessfully) on MATH.SE first.
As a bit of background: one way to study the mechanics of deformation of a continuous ...
- 81
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1
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334
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Prevalence of B-fields
I am wondering how B-fields, which are basic objects in Generalized Geometry, relate to the B-fields of Ben's question and the answers to it.
In Generalized Geometry, the B-field is a (1,1)-form, and ...
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What is the precise relationship between real Poisson algebras and commutative $C^*$ algebras?
I've been teaching myself quantum mechanics, and I realized that I'm missing something fundamental. Namely, there are two pictures that I don't know how to reconcile:
Quantum Mechanics generalizes ...
- 2,071
3
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1
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212
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Monotile that tiles when you apply a rubber band
My (non-mathematician) friend asked me a physics/tilings question that maybe someone here is interested in dissecting, or can point to the literature if this problem has been studied.
Does there ...
- 6,652
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A particular contour integral
Mathoverflow,
I'd like to carry out the following integral,
$$f(t) = \int_{- \infty}^{\infty}\frac{-i\Omega e^{i \Omega t}}{1-\sqrt{-i\Omega}\coth(\sqrt{-i\Omega})} d\Omega.$$
Here's what I've ...
3
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1
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212
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Three body problem with point interactions
I've studied the HVZ theorem for the three body problem interacting with regular potentials. I'd like to extend this result to the three body problem with point interactions (delta potentials).
Is ...
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Interesting question about the Thomson problem for arbitrary number of electrons
This question is crossposted from here I believe this is a pretty hard question and so I decided to repost the question in the Math Overflow forum. If there is something wrong with doing this, I am ...
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inclusion of von Neumann algebras implies reversing inequality of its modular operators
I'm working with von Neumann algebras and I stumbled with this statement in a work of Borchers (1999)
Since $\mathcal N \subseteq \mathcal M$, it follows by standard arguments that $\Delta_{\mathcal ...
- 424
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214
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How to calculate the integral of a product of a spherical Hankel function with associated Legendre polynomials
From numerical experiments in Mathematica, I have found the following expression for the integral:
$$
\int_{-1}^{1}h_{n}^{(1)}\left(\sqrt{a^{2}+b^{2}+2ab\tau}\right)P_{n}^{m}\left(\frac{a\tau+b}{\sqrt{...
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Are square configurations the only critical points of the energy on the circle?
$\newcommand{\S}{\mathbb{S}^1}$
$\newcommand{\la}{\lambda}$Let$$M=\{(x_1,x_2,x_3,x_4) \in (\S)^4\,\, |\,\, \text{ all the } x_i \, \text{ are distinct}\} $$
Define $E:M \to \mathbb{R}$ by
$$E(x_1,x_2,...
- 6,741
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geometrical or physical interpretation of second Chern classes of Calabi-Yau threefold
It's my first post.
Consider Calabi-Yau threefold $M$ and its tangent bundle $TM$. I know $c_1(TM)=0$ means metric on $M$ is a solution of vacuum Einstein equation. Then my question is "are there any ...
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Does there exist a compactly supported integrable function with infinite Coulomb energy?
The title of the question pretty much says it all. I am looking for a function $f\in L^1(\Omega)$, where $\Omega \subset \mathbb{R}^3$ is a bounded domain, such that
$$
E[f] = \iint\limits_{\Omega\...
- 401
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Partial Liouville equation
In my master's thesis, I worked on mathematical multi-scale models for muscle tissue. Now after finishing it, I would like to find out if one direction could be a research topic for my PhD.
At one ...
3
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Multiplicativity of $\zeta$-function regularized determinant
Let $A$ be a selfadjoint elliptic differential operator on a compact manifold. In mathematical physics and differential topology one often defines its determinant using the $\zeta$-function ...
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Is there any connection between Lagrange points and the icosahedron?
Given the Newtonian two-body problem, one can ask if there are any orbits that allow a test particle to maintain a fixed configuration relative to the two bodies. In other words, in a frame that ...
- 1,444
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654
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In the topos-theoretic interpretation of Physics by Isham & Doering what role does intuitionistic logic play? [closed]
I've asked this question on Physics.SE but was advised to ask it here.
Isham & Doering have written a series of papers exploring how to ground physics in topoi. Now the internal logic of topoi is ...
- 2,369
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What is the relationship between complex time singularities and UV fixed points?
In this paper it is described how the turbulent kinetic energy spectrum and the flatness (a measure for intermittency) are governed by the position of the (dominant) singularities of the solutions of ...
- 418
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Children's drawings and Seiberg-Witten curves
This physics (bear with me for a while) paper seems to say something about Gal \bar Q/Q:
Children's Drawings From Seiberg-Witten Curves, hep-th/061108.
Let's ...
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Deriving the Mercator projection algorithm
The standard model of Mercator projection shows a cylinder wrapped around a spherical earth eg Wiki.
Many sites describe the resulting square map like this:
"...spherical Mercator maps use an extent ...
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Examples of ODEs with complex constant coefficients and applications to physics?
This question is asked on stackexchange: Are there examples for ODEs with complex coefficients with applications in physics?
but received no answers. I am reposting it here on the hope that it catches ...
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PDE’s whose solutions can be presented using path integrals
It is well known that solutions of the Schroedinger equation and of the heat equation can be presented using path integrals:
$$\psi(x,t)=\int K(x,t;y,0)\psi(y,0)dy,$$
where the kernel $K(x,t;y,0)$ is ...
- 21.8k
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1
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Applications of Generalized Geometry to Theoretical Physics [closed]
I'm looking for some topics on Generalized Geometry applied to Physics for a master thesis. I took an introductory course last year, and I have a degree in both Mathematics and Physics. I would ...
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489
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Proof of generalized Cauchy formula
I would like to know if there is a proof for the identity used in the superconformal index of 4d ${\cal N}=2$ gauge theory. In the paper by Rastelli el al, it was discovered that Eq. (10) is equal to ...
- 2,273
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David Hilbert on Complex Multiplication [closed]
I have tried vainly to understand the significance of the following statement attributed to David Hilbert:
The theory of complex multiplication is not only the most beautiful part of mathematics ...
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Derivation of Bessel functions
I am writing a summary on a work on Fluid Dynamics that develops irrotational flow states that appear to interact amongst each other according to the equations of Electromagnetism http://arxiv.org/abs/...
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4
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EM-wave equation in matter from Lagrangian
Note
I am not sure if this post is of relevance for this platform, but I already asked the question in Physics Stack Exchange and in Mathematics Stack Exchange without success.
Setup
Let's suppose a ...
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Generating Functional for the Dirac Field, equivalence of expressions
As with the Klein-Gordon field, we can alternatively derive the Feynman rules with the free Dirac theory by means of a generating functional. In analogy with the scalar field theory where $Z[J]$ is ...
user78817
2
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What is the "fundamental theorem of invariant theory" ?
The basic question I guess can be formulated as - given two integers $N_f$ and $N_c$ what are the ways in which the fundamental and the anti-fundamental representations of $U(N_f)$ be combined to get ...
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Vacuum state generating functional
In Theorem 1 of this paper Segal stablish a relation between states and generating functionals.
He assert that in order to $\mu$ be a generating functional must satisfy
$$
\sum_{j,k\in F} \mu (z_j-...
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1
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Sufficient conditions for unitarity of a representation of a Lie Superalgebra
Suppose we have a Lie superalgebra with triangular decomposition:
\begin{equation}
\mathfrak{g} = \mathfrak{g}^{+} \oplus \mathfrak{g}^{0} \oplus \mathfrak{g}^{-}
\end{equation}
I've seen it stated ...
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Approximate solutions to $x''(t)=-cx + f(t)x$
I recently studied a problem which involved two particles joined by a harmonic spring moving in a potential and through some manipulation, I obtained the equation
$x''(t) = -\omega^2x + f(t)x$,
where $...
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Is there an example Hamiltonian that is uncomputable?
In a paper from 2015 Toby S. Cubitt et al showed that the problem of determining the existence of a band gap in the excitation spectrum of a quantum many-body system, was undecidable. This result ...
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What is the relationship between Riemannian and sympletic musical isomorphisms on the cotangent bundle?
Let $M$ be a smooth manifold. Its cotangent bundle naturally has a symplectic structure, and this gives rise to musical isomorphisms. These musical isomorphisms are the ones from physics that relate ...
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Difference Between Total Least Squares Plane and Plane Orthogonal to Principal Axis of Inertia Tensor
Given a finite set $P$ of points in $\mathbb{E}^3$ , one can calculate an approximating plane either as the solution of a Total Least Squares problem or by interpreting the problem physically, ...
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131
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Questions about using mathematical methods to prove the Caratheodory's Concept of Temperature
Caratheodory's Concept of Temperature is not Carathéodory's theorem.
I have tried,but I found nothing about this question by searching online.
This is what I have seen in a thermodynamics textbook; ...
- 21
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99
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1D Schrödinger Equation with Measure-Valued Coefficients
I've been looking at one of the simplest systems I can think of: a one-dimensional infinite square well on $[0,1]$ with Hamiltonian given by the following:
$$\hat{H}=-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}...
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