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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.

2
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1answer
26 views

Complex conjugated representation and its Young tableaux

This post is an exact copy of one that I posted in Math's site. I do this copy because people there suggested me to do it since, apparentely, in Mathematics and Physics we use different conventions ...
0
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0answers
25 views

Levi-Civita identity [on hold]

with Einstein summation convention What's my problem?
-1
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0answers
42 views

Does physics allow for anything other than a mathematical reality? [on hold]

The answer I am looking for may be contained in this article: Tegmark: Mathematical universe hypothesis, but frankly, I can't follow it in enough detail. I appreciate this question may be viewed as ...
0
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0answers
23 views

Torsion Tensor covariant and contravariant

I want to know the relation between covariant and contravariant torsion tensors. Also please tell me that can we change the order of indices in torsion tensor?
0
votes
0answers
22 views

Simply Connected Spaces [closed]

Informally, an object in our space is simply connected if it consists of one piece and does not have any "holes" that pass all the way through it. For example, neither a doughnut nor a coffee cup (...
4
votes
0answers
66 views

Why do we assume wavefunctions to be finite and continuous everywhere? [duplicate]

Why do we assume the wavefunctions to be everywhere finite and continuous? Finiteness maybe required due to square integrability but why continuous? Such a restriction is not imposed on its derivative....
2
votes
0answers
74 views

Euler-Maclaurin formula for path integral

Is there a corresponding Euler-Maclaurin formula for path integral when we divide the path integral into discrete lattice? What is the error correction when we divide the space into lattice of length ...
2
votes
1answer
68 views

Fourier transform property in Feynman 1986 Dirac Memorial Lecture

In his famous 1986 Dirac Memorial Lecture, Feynman refers to a Fourier transforms theorem holding in case F(w) satisfies "certain properties", while being restricted to positive frequencies only: ...
0
votes
0answers
31 views

Integrals formulae in two dimension [migrated]

I come across the following two integral formulae The first integral formula is \begin{equation} \int_C d^2z |z|^{2a}|z-x|^{2c}|z-1|^{2b} = \frac{S(a)S(c)}{S(a+c)}|I_{0x}|^2+\frac{S(b)S(a+b+c)}{S(a+...
1
vote
1answer
44 views

Fourier transform of derivative of plane wave [closed]

What is the Fourier transform $F(k)$ of: $$ f(y) = A \, ik \, e^{iky} $$ If you calculate it with Wolfram Alpha, it says that there are no results found in terms of standard functions.
-1
votes
1answer
25 views

Need some help to show this relationship using parseval's theorem [closed]

Use Parseval’s theorem for the Fourier series and take L → ∞ to show that:
-1
votes
2answers
97 views

Can we create new physics through moderately brute force computing? [closed]

So my argument for this is that the expansion of knowledge in any field of physics depends on what is previously known, and what we physicists express or knowledge as equations. So here's what I ...
1
vote
1answer
64 views

Representing a reducible Cartesian tensor as a spherical tensor

I'm quite confused by this transformation, and am trying to gain fluency in moving back and forth between these objects. I understand that a second order dyadic Cartesian tensor can be represented as ...
0
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0answers
27 views

Rigorous Treatment of Quantum Tensor Operators

Recently, my classes have introduced me to the idea of spherical tensors and the Wigner-Eckart (WE) Theorem, but my previous classes on tensors had emphasis on things like covariance, contravariance, ...
1
vote
1answer
34 views

Electric Flux of A Point Charge Derivation

I am trying to understand the derivation of Gauss's Law and came across this line describing the electric flux through a small area of a sphere from a point charge: Source $$ E\cdot\Delta A_i = E_n\...
-1
votes
1answer
56 views

Mathematics textbooks to understand Jackson electrodynamics

I want a very solid mathematics background that will make going through Jackson's text less challenging. What books would you recommend?
0
votes
1answer
27 views

Electric field on the boundary of a continuous charge distribution

In Purcell and Morin's Electricity and Magnetism, 3rd Edition, the claim is made that the magnitude of the electric field on the boundary of a continuous charge distribution is finite (assuming the ...
11
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7answers
900 views

Can we divide a vector by another vector? How about this: $a = vdv/dx?$

My physics teacher told us that we can’t divide vectors, that vector division has no physical meaning or significance. How about this: $$a = vdv/dx.$$ It says acceleration vector equals velocity (as ...
0
votes
1answer
55 views

Is it necessary to learn complex analysis in order to learn classical electrodynamics?

I am reading "Classical electricity and magnetism, chapter 1" by Wolfgang K. H. Panofsky and Melba Phillips. I am having little trouble on page 13 and afterwards. It talks about singularity, poles, $2^...
0
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0answers
28 views

Relation between computation of curl and divergence and their formal definitions

both divergence and curl of a vector field have a formal definition, however, we don't use these definitions when we compute the divergence or curl. so can we just derive the computations from the ...
0
votes
2answers
66 views

Is gravitational constant a rational number? [duplicate]

The question is the title. But I'm quite doubtful if this question is meaningful or not. Since this constant is obtained by experiment, we can never know its exact value, unlike $π$ or $e$. Is it ...
1
vote
0answers
70 views

What optical system could perform a multiplication/convolution of several rectangular pulses with different widths?

Statement There is a following multiplication/convolution of $n$ rectangular pulses with different widths $$ f(x)=\mathrm{rect}(c_1x)\ast\mathrm{rect}(c_2x)\ast\ldots\ast\mathrm{rect}(c_mx) $$ or $$ ...
1
vote
0answers
67 views

Pure math courses for physicists: Topology [closed]

I'm in my bachelor in physics. In a couple of weeks I start my last year, and I'm interested in taking some pure math courses. As you see, I like the theoretical point of view, but I don't know if the ...
0
votes
1answer
21 views

Normalising angled Earth magnetic field

Me and my team are participating in ESA Astro Pi challenge. Our program will ran on the ISS for 3 hours and we will our results back and analyze them. We want to investigate the connection between ...
0
votes
1answer
36 views

Is the Jacobian different for different ${\cal L}^p$ norms?

(I posted this to the math stackexchange, but I've yet to receive an answer so I figured I should post here too, as this forum seems faster to respond and is full of knowledgable people.) Because the ...
1
vote
0answers
25 views

conventional matrix notation for distance interval

Why matrix notation for distance interval is represented by this? $$g_{\mu \nu}\Delta X^{\mu}\Delta X^{\nu}=(\Delta X)^Tg (\Delta X)=\Delta X^{\mu}\Delta X^{\nu}g_{\mu \nu}$$ Could you explain ...
5
votes
2answers
128 views

Would a commutative power operator simplify some equations of physics? [closed]

Hypertype Theory makes the radical suggestion that a commutative power operator would be preferable to the traditional non-commutative power operator $a^b$. Are there any equations in physics that ...
15
votes
4answers
2k views

The reasoning behind doing series expansions and approximating functions in physics

It is usual in physics, that when we have a variable that is very small or very large we do a power series expansion of the function of that variable, and eliminate the high order terms, but my ...
0
votes
2answers
75 views

How is the wave function Lebesgue integrable?

Let's assume we have a plane wave $\psi(x,t)= A_{0}e^{i(kx-wt)}$ in position space. To find the momentum representation of this wave we'd apply the Fourier transform. However, I don't see how this is ...
0
votes
1answer
27 views

Smoothness of sum over histories?

Considering the sum over histories approach to quantum mechanics. This considers all histories consistent with certain starting configurations and ending configurations. How "smooth" do these ...
2
votes
0answers
48 views

Polylogarithmic integrals

NB: I was sent here from Math.SE, stating that polylog integrals are more common in physics and someone here might have an answer. I have asked in Phys.SE chat whether it was okay to post here but no ...
1
vote
2answers
86 views

Math needed for plasma physics? [closed]

I am curious about what kind of math is needed for studying plasma physics, especially for the magnetohrodynamics. I know there are lots of PDEs in plasma physics, but how about real analysis? Or ...
0
votes
1answer
33 views

Application of linear constant coefficients ODE of the second order [closed]

I've asked this question in math forum. Apparently this question is not welcomed there. So maybe here I can get a proper response. Consider ODE in the form of $$y''+ay'+by=f(t)$$ where $a$ and $b$ are ...
1
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0answers
65 views

Learning quantum mechanics with a strong mathematics background [closed]

Quick pedagogical question. If one were to have a substantial mathematics background prior to taking a undergraduate physics course in quantum mechanics, (say Grad. Real Analysis, Algebra, ...
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votes
2answers
81 views

Dispersion Relations in Particle Physics [closed]

Please tell me how to get the identity(2) in this image
3
votes
2answers
136 views

Does Euler number $e$ have a role in kinematics?

Euler number $e$ is often explained with the example of compound continuous interest. I was wondering if it could also be illustrated with an example about the displacement of a body (although not an ...
2
votes
1answer
55 views

Is there a simple way to explain a fundamental representation of $O(N)$?

Is there a simple way to explain fundamental representation in Physics? For example, a fundamental representation of $O(N)$?
1
vote
1answer
134 views

Paths contributing to the path integral measure in Gross' book

My question regards a comment D. Gross makes in his unpublished lecture notes about quantum field theory (the one with no chapter 1). In chapter 8 (path integrals) pag. 136, he reaches at the ...
2
votes
0answers
43 views

Is 1/vector is a vector or not? [duplicate]

Let $\vec { A } = a \hat { i } + b \hat { j } + c \hat { k }$. Is $\frac { 1 } { \vec { A } }$ a vector or not, and if it is, then what are its components?"
3
votes
1answer
47 views

Theories, Corollaries, and Models

I apologize if this question seems overly basic. I was wondering how to recognize what a theory is really saying, as opposed to the explanation/corollaries that are drawn from it. As an example, take ...
0
votes
1answer
20 views

Scalar field and 2 types of line integrals

Consider the line integral, $\int _ c$f(x,y)$\vec dr$ , where $f(x,y)$ is a scalar field, and it is evaluvated on a curve $c $. After integration we get a vector let it be $\vec I$ . $\int _ c$f(x,...
1
vote
0answers
65 views

Extensors in mathematics and in physics [closed]

Could someone explain in a simple but accurate manner what extensors are as mathematical entities and how they are used? How do extensors essentially differ from tensors? Are there or could there be ...
3
votes
0answers
80 views

Geometry of Affine Kac-Moody Algebras

One can reconstruct the unitary irreducible representations of compact Lie groups very beautifully in geometric quantization, using the Kähler structure of various $G/H$ spaces. Can one perform a ...
4
votes
2answers
172 views

Are characteristics the only solution to the advection equation in 1+1D?

I'm currently reading about fluid dynamics and the Riemann problem, and a very commonly used equation to introduce the topic is the 1+1D advection equation with constant coefficient $v$: $$ \frac{\...
1
vote
1answer
90 views

Proving a Mathematical hypothesis using Physics [closed]

I've asked the question below on mathexchange here about 2 weeks ago. while I did not satisfied with the comments and answer there specially because the lack of examples and references that I was ...
0
votes
1answer
309 views

Convert sexagesimal to decimal

I've been studying astronomy and I've encountered 3 different (sexagesimal) ways to write angles. hh mm ss - hours minutes and seconds dd '' '''' - degrees, arcminutes and arcseconds. +/- dd mm ss -...
0
votes
1answer
48 views

Why do we require that functions which parametrize gauge transformation are smooth?

A local $U(1)$ transformation is given by \begin{equation} f(x) = e^{i\epsilon(x)} \qquad \text{with} \qquad \epsilon(x) \in C^\infty \, . \end{equation} Why do we require that the functions in ...
0
votes
2answers
83 views

Do we know, or at least have a strong argument for the fact that for a given time interval, we can always find a smaller time interval? [duplicate]

Motivation: In Biology, when, for example, biologists try to model the population dynamics of a population, they say: Let $N: \mathbb{R}^{nn} \to \mathbb{R}^{nn}$ be a function that represents ...
1
vote
1answer
172 views

Could a quantum computer calculate the values of the riemann zeta that are currently out of reach with classical computers?

Could a quantum computer calculate the values of the Riemann zeta function that are currently out of reach with classical computers? Any counterexamples to the RH would be somewhere in the range ...
0
votes
0answers
26 views

How to decide step size(sigma value) in MCMC routine related Cosmological Parameter estimation?

I am running a modified Lambda-CDM in MCMC routine using Montepython and CLASS code, with aim to extract parameter values from Planck data. In addition to the original 10-15 parameters for Planck ...