# Tagged Questions

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 ...

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### String theory from a mathematical point of view

I have a great interest in the area of string theory, but since I am more focused on mathematics, I was wondering if there is any book out there that covers mathematical aspects of string theory. I ...
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### Why does calculus of variations work?

How does it make sense to vary the position and the velocity independently? Edit: Velocity is the derivative of position, so how can you treat them as independent variables? Doesn't every physics ...
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### Radial quantum number for infinite circular well

For completeness, I will sketch the solution of a particle in an infinite circular well first and then get to my question. I apologize in advance since the introduction is standard undergraduate ...
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### What is the correct relativistic distribution function?

General Statement and Questions I am trying to figure out the proper way to model a velocity/momentum distribution function that is correct in the relativistic limit. I would like to determine/know ...
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### Tension in string

In the derivation of the 1d linear wave equation for small amplitude waves on 1d string, they said at the end that if the density $\rho(x)$ is assumed to be constant, then the Tension $T(t)$ would ...
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### Physics : Formula involving density, Mass, temperature and pressure [closed]

A set of dryers has a mass 40kg and density of 16kg/m3 at temperature of 40°C under the pressure 760mmHg. At what temperature will the mass be 50kg with density 20kg/m3 under a pressure of 700mmHg
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### What does unphyisical quantity mean? [closed]

I was reading this Terry Tao article and almost near the end he says "the terms involving infinity do not make particularly rigorous sense, but would be considered orthogonal to the application at ...
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### response function and Fourier transform

A response function defined as the kernel of the following integral: $\rho(t) = \int_{-\infty}^t \chi(t,t') E(t')dt'$ (1), where $\chi(t,t')$ is the response function. Physically, it relates ...
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### Derivation of Schwarzschild metric using the full machinery of differential geometry [closed]

How would one derive the Schwarzschild metric using the full machinery of differential geometry, using the component approach as little as possible? Something along these lines: Begin with a manifold ...
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### Don't understand the integral over the square of the Dirac delta function

In Griffiths' Intro to QM [1] he gives the eigenfunctions of the Hermitian operator $\hat{x}=x$ as being $$g_{\lambda}\left(x\right)~=~B_{\lambda}\delta\left(x-\lambda\right)$$ (cf. last formula on ...
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### A question about the uniqueness of Riesz representation theorem

I am sorry this question may be too math related. However, I come from physics background and I would like to ask for an physicist's explanation. As far as I know, the Riesz representation theorem ...
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### What is Motivic mathematics and how is it used in physics?

In a few videos I've seen where he discusses the new approach to calculating the super Yang Mills scattering amplitudes, Nima Arkani-Hamed sometimes alludes to the use of Motivic methods as being ...
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### “Velvet way” to Grassmann numbers

In my opinion, the Grassmann number "apparatus" is one of the least intuitive things in modern physics. I remember that it took a lot of effort when I was studying this. The problem was not in the ...
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### Floquet quasienergy spectrum, continuous or discrete?

I haven't got a feeling about Floquet quasienergy, although it is talked by many people these days. Floquet theorem: Consider a Hamiltonian which is time periodic $H(t)=H(t+\tau)$. The ...
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### Motivation for the use of Tsallis entropy

Every now and again I hear something about Tsallis entropy, $$S_q(\{p_i\}) = \frac{1}{q-1}\left( 1- \sum_i p_i^q \right), \tag{1}$$ and I decided to finally get around to investigating it. I haven't ...
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### Mathematics of Surface Divergence and Surface Curl

While studying electrodynamics I found two functions - Surface Divergence and Surface Curl - that seem to condense the formulas for superficial discontinuities of the electric and magnetic fields ...
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### Physic explanation of some property of heat equation? [closed]

When I compute the heat equation, I found that gross of heat do not change,it is same as our real world.But as I know , the heat equation is found according to the way of heat conduction. Why the ...
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### Spectrum of Laplacian on one hemisphere

as is well-known, the spectrum of the Laplace operator on $S^2$, computed via $-\Delta f=\lambda f$, is positive and discrete. What happens to the spectrum if we just take one hemisphere into account?...
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### The change in time of a concentration in a fluid can be described by Reynolds' theorem. Is that the whole story?

Let $d\in\left\{2,3\right\}$ and $\Omega_t\subseteq\mathbb R^d$ be the bounded set occupied by a fluid at time $t\ge 0$. Moreover, let $\eta_t:\Omega_t\to[0,\infty)$ be the concentration of imaginary ...
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### Are there applications of $L_p$ spaces in quantum mechanics?

In quantum mechanics, there a lot of emphasis on $L^2$ spaces since Hilbert spaces describe states in quantum mechanics, so we have $$\langle \psi | \psi \rangle = \int |\psi^2(x)|\, dx$$ Even ...
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### Proof that fixed points of a null field are zero

Suppose we have a scalar field $V$ (which can be acoustic pressure, or a scalar electric potential) that is a solution of the wave equation $$\Box V(x,y,z,t) = 0$$ I am wondering if a fixed (non-...
I need to show that for $F(x_1, .., x_n)$, the Legendre transformation is, $$G(s_1, ..., s_n) = \sum_{i}^{N} x_i s_i - F$$ where $$s_i = \frac{\partial F}{\partial x_i}$$ and has the property that $$... 1answer 171 views ### Not satisfied with “trick” in zeta function regularization I am not satisfied with the explanations of$$\sum_n \log \lambda_n = - \frac{d}{ds} \sum_n \lambda_n^{-s}\bigg|_{s=0}$$"trick" used in zeta function regularization, discussed here and here, or the ... 1answer 260 views ### L^{1} energy-momentum tensors in general relativity; semi-classical gravity I was unsure whether to pose this question in a physics or mathematics forum, but it is an interesting idea I have been thinking about for some time. In any (semi-)classical field theory it is often ... 0answers 55 views ### Is time-1 map of a Hamiltonian vector field on a cylinder always twist? I have a one degree of freedom analytic Hamiltonian H(q,p) defined on a semi-infinite cylinder, i.e. (q,p) \in \mathbb{T} \times \mathbb{R}^{+}, such that all level sets H(q,p)=c are closed ... 1answer 47 views ### Angular momentum partial components of a k-dependent pairing potential I am going over this review on pairing in unconventional superconductors :http://arxiv.org/abs/1305.4609v3 which on page 21 states that for a "regular" function U(\theta), partial components U_l ... 0answers 1k views ### Linear sigma models and integrable systems I'm a mathematician who recently became very interested in questions related to mathematical physics but somehow, I already have difficulties in penetrating the literature... I'd highly appreciate any ... 5answers 1k views ### What happened with Hilbert's sixth problem (the axiomatization of physics) after Gödel's work? I'll write the question but I'm not fully confident of the premises I'm making here. I'm sorry if my proposal is too silly. Hilbert's sixth problem consisted roughly about finding axioms for physics (... 0answers 44 views ### Expansion of comparator Currently I am working on Pesking Schroeder Section 15.1 and trying to understand the expansion given in (15.5), which is$$ U(x+\epsilon n, x) = 1 - i\,e\,\epsilon\,n^{\mu}\,A_{\mu}(x)+O(\epsilon^2) $... 1answer 1k views ### Equation of a torus In the recent paper http://arxiv.org/abs/1509.03612, page 37. They say that a torus can be described by the equation $$y^2=x(z-x)(1-x)$$ where$x$is a coordinate on the base$\mathbb{P}_1$. Could ... 1answer 123 views ### In the algebraic formulation of Quantum Mechanics, how do probability amplitudes naturally arise? In the algebraic formulation of quantum mechanics, consider$\mathcal{B}(\mathcal{H})$as the set of all bounded operators on$\mathcal{H}$(with involution, norm, etc.), which form a C*-algebra$C$. ... 3answers 1k views ### Books for linear operator and spectral theory I need some books to learn the basis of linear operator theory and the spectral theory with, if it's possible, physics application to quantum mechanics. Can somebody help me? 1answer 70 views ### Maxwell Boltzmann distribution: Going from momentum to energy I am learning about the Maxwell Boltzmann distribution, and am trying to convert the equation from momentum into energy, but I'm stuck on changing$d^n p$into$dE$. I have the equation: $$E=\frac{|\... 1answer 59 views ### Optics Diffraction Grating Plot I was unsure whether to post this in physics stackexchange or mathematica stackexchange, so I posted it in both. I'm trying make an intensity plot for a diffraction grating that contains 100 lines/mm.... 10answers 4k views ### Physics for mathematicians How and from where does a mathematician learn physics from a mathematical stand point? I am reading the book by Spivak Elementary Mechanics from a mathematicians view point. The first couple of pages ... 3answers 1k views ### What is a good introduction to integrable models in physics? I would be interested in a good mathematician-friendly introduction to integrable models in physics, either a book or expository article. Related MathOverflow question: what-is-an-integrable-system. 4answers 988 views ### Can momentum have a complex expectation value? I'm making examples of wave functions to incorporate in a QM exam. I came up with the following wave function, which gives me some troubles:$$\psi(x,0) = \begin{cases} A(a-x), & -a \leq x \leq a\... 3answers 6k views ### Mathematically-oriented Treatment of General Relativity Can someone suggest a textbook that treats general relativity from a rigorous mathematical perspective? Ideally, such a book would Prove all theorems used. Use modern "mathematical notation" as ... 0answers 77 views ### Experiments to resolve dillema between continuity and discrete Which experiments/experimental methods are suggested to resolve an alternative about the structure of our universe space and time - is it continuous or is it discrete in a very small scale, especially ... 1answer 49 views ### Time dependent electric field: Mathematical expansion for local electric field In many articles and books I see that local electric field is expanded as $$\vec E_0(\vec r(t)) = \vec E_0(\vec R_0) − (\vec a(t) \cdot \nabla) \vec E_0(\vec R_0) \cos(\Omega t) + \ldots$$ For ... 1answer 111 views ### Can binary sequences generated from ergodic maps be chaotic? Briefly, the way symbols are generated is: Consider a one-dimensional chaotic map$T: [0,1]→[0,1]$and a time series$\{x_n\}_{n=1}^N$generated with this map. Define a threshold$Aand a ... 1answer 79 views ### How do we take the limit of this quantum operation? I am wondering how to take the following limit: \begin{align} L= \lim_{\tau \to \infty} \frac{1}{\tau} \int_{-\tau/2}^{\tau/2} dy \, \left(1 - \frac{1}{\sqrt{ \pi} \sigma } \int_{-\tau/2}^{\tau/2}... 0answers 148 views ### Cones with deficit angle 2\pi\$ and euler characteristics
I've managed to confuse myself with cones and deficit angles. Let's consider a conical defect in 2 dimensions. So the metric is the usual one in polar coordinates, $$ds^2 = dr^2 + r^2 d\phi^2,$$ ...