# Questions tagged [mathematics]

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 The mathematics tag covers non-applied pure mathematical disciplines that are traditionally not part of the mathematical physics curriculum, such as, e.g., number theory, category theory, algebraic geometry, general topology, algebraic topology, etc.

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### Good math books for basic physics [closed]

I am good at math, but bad at applying it. Is there any book which goes over math being applied for basic physics primarily motion?
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### Would it be valid to say $y \propto 2x$ instead of $y \propto x$?

Would it be acceptable to write $y \propto 2x$ or would it be wrong to add the $2$? I just want to describe a relationship in more detail.
1 vote
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### Does the exponential representation of Dirac delta function depend on choice of Fourier convention?

Is it always true that $$\delta(\omega) = \frac{1}{2\pi}\int_{-\infty}^{+\infty} e^{i \omega t} dt ,$$ regardless of your Fourier convention? For example, if I choose to use the Fourier convention ...
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### Wigner-Eckart for Finite groups

We know the Wigner-Eckart theorem generalizes to say $\mathrm{SU}(3)$ (see for example this answer). In a different direction, I am curious if/how it generalizes to finite groups of $\mathrm{SU}(2)$. ...
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### What does the notation $d𝜏'$ mean?

$\text{I was studying helmotz theorem and saw this notation, what does it mean? How is d}\tau' \, \text{ different from d}\tau \text{?}$ From :- David J. Griffiths-Introduction to Electrodynamics-...
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How does the identity $$\epsilon^{prst}A_{ip}A_{kr}A_{ls}A_{mt}=-A\epsilon_{iklm}$$ with the Levi Civita symbol $\epsilon$ and the determinant A of the matrix $A_{ik}$ follow from the equation $$\... • 61 1 vote 2 answers 76 views ### Static solution to an implicitly dynamic problem - heat equation Heat equation This is the heat equation:  \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2}  ... • 123 -2 votes 1 answer 156 views ### Exact definition of divergence. Is it really the dot product of nabla operator with a vector? [closed] I was trying to understand the derivation for divergence in cylindrical and spherical coordinate system, and I am a bit confused here. https://www.gradplus.pro/deriving-divergence-in-cylindrical-and-... • 33 0 votes 0 answers 54 views ### When can I commute the 4-gradient and the "space-time" integral? Let's say I have the following situation$$I = \dfrac{\partial}{\partial x^{\alpha}}\int e^{k_{\mu}x^{\mu}} \;d^4kWould I be able to commute the integral and the partial derivative? If so, why is ... 1 vote 1 answer 64 views ### Material to Study the Definition, Algebra, and Use of Infinitesimals in Physics [closed] This is going to be a rather general question about suggestions on best supplementary material to properly explain the use of infinitesimals (or differentials?) for the purposes of integration or ... 0 votes 1 answer 31 views ### Differentiation of a product of functions If I have three (vector)functions, all dependent on different (complex)variables: a = X^{\mu_1}(z_1, \bar{z}_1), b = X^{\mu_2}(z_2, \bar{z}_2), c= X^{\mu_3}(z_3, \bar{z}_3) \end{... • 41 3 votes 0 answers 41 views ### Proof Majorana spinors exists if maximal commutant of Clifford algebra is \mathbb{R} I am searching for a proof of the claim made in this post. It states that Majorana spinors (I refer to both complex pinor and spinor representations which are restricted to the real Spin group and ... 1 vote 0 answers 65 views ### What is the Taylor series of the expectation value of an observable in quantum mechanics? [closed] I recently came across a form of the expectation value of an observable, but a Taylor series (I think?) was taken up to second-order: \langle O\rangle = \langle O\rangle_{C=0} + \... • 19 1 vote 0 answers 76 views ### Motivation behind reflection positivity I have taken a look at this physicsSE question, Wikipedia, and this paper by Jaffe which go over reflection positivity. While they all nicely explain the definition behind reflection positivity and ... • 3,370 2 votes 2 answers 201 views ### Can the composition law of a group be defined only when considering a representation or realisation of the Group? When we talk about, lets say, the Lorentz group, we define the action of the Lorentz transformation \varLambda on \begin{alignat}{1} x^{\mu} & \in\mathbb{R}^{1,3},\\ x^{\mu} & \rightarrow x'^... 3 votes 2 answers 83 views ### In what sense is \int (u \cdot \nabla) u \cdot u dx an energy flux? Due to the nature of this question I have have cross-listed it on mathSE. Let u be either a solution to either the Euler equations or Navier-Stokes equations over a domain \Omega. In fluid ... • 3,370 0 votes 1 answer 107 views ### Mathematical meaning of a position eigenbra \langle x_0 | Let |x_0\rangle be an position eigenket. The physical picture I have for |x_0\rangle is a particle located at x_0. Thus it should be represented by a delta function \delta(x-x_0). For f\in L^... • 3,370 1 vote 1 answer 69 views ### Is there an error bound for perturbation theory? It is usually said that perturbation theory is valid when the perturbation is much smaller than the spacing between energy levels. However, I was thinking whether there exists an rigorous error bound. ... • 689 2 votes 0 answers 28 views ### Implications of quantized space (a la LQG) on defining "realistic" number systems [duplicate] Disclaimer: not a professional physicist or mathematician, so (deserved) tomato-throwing is welcome. I've been pondering the "naturalness" of real numbers for some time now, in the sense of ... • 121 0 votes 1 answer 58 views ### Stokes' theorem and vector continuity equations I have been working with homogeneous continuity equations of the general form:\frac{\partial \rho}{\partial t}+\vec{\nabla}\cdot \vec{J}=0$$This has me wondering whether we can formulate other ... • 1,616 1 vote 2 answers 126 views ### Why does a singularity imply the need for a distribution? I am following Section 11 of Prof. Etingof's MIT OpenCourseWare notes on "Geometry And Quantum Field Theory" in which he says: ...for d = 1, the Green's function G(x) is continuous at ... • 3,370 1 vote 1 answer 51 views ### On complex impedance representation and Riemann surfaces We know that a complex number, z=re^{i\phi}, can be represented with infinitely many phases, \phi+2\pi n, for integer n, as can be easily seen from the equivalent picture of a vector on the ... • 632 4 votes 2 answers 714 views ### Wrong solution for Green function of one-dimensional Poisson equation An old electrodynamics exam question asks: "Find the Green function (for the one-dimensional Poisson equation) that solves the equation$$ \frac{d^2}{dx^2}G(x,x') = -\delta(x-x'). $$Choose the ... • 151 -5 votes 1 answer 137 views ### Manipulation of functions inside a Dirac Delta function [closed] It is not clear to me how this derivation proceeds through the steps. Could someone help me understand how to arrive at this result or point me towards a resource that explains these algebraic ... 0 votes 2 answers 81 views ### Solving a PDE using x-vt as a variable So I was reading this Landau and Lifshitz paper: https://doi.org/10.1016/B978-0-08-036364-6.50008-9 The article can also be found without a paywall by just searching its title, "On the Theory of ... 1 vote 1 answer 40 views ### Electric field at a point created by a charged object (derivation/integration process) I was hoping someone can help me understand the math behind the electric field (electrostatics). I have gaps in my knowledge about integrals and derivatives (university moves very quickly and it has ... • 19 -8 votes 3 answers 217 views ### How Taylor series is compatible with special relativity? In mathematics, an analytic function is defined by its possession of a Taylor series with a positive radius of convergence (R_c​>0). Notably, certain analytic functions—such as holomorphic ... • 342 0 votes 0 answers 46 views ### Arc length between configurations in the "mass distance" In classical Lagrangian mechanics, the mass M is a Riemannian metric on the configuration space Q. Does the "arc length" of a path \gamma : [0, 1] \to Q,$$ \int_0^1 {\lVert{\gamma'(t)}...
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I have been reading Introduction to Electrodynamics - Griffiths about solving Laplace equation in cartesian coordinates, and in that book, I saw this statement: The functions $\sin(n\pi y/a)$ are ...