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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.

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I know many students with a major in physics don't learn mathematics rigorously, but they can understand for example electromagnetism. Why? [on hold]

I am very poor at physics but I wanna know basic physics. And I like mathematics, although I am not very good at mathematics. I know many students with a major in physics don't learn mathematics ...
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2answers
59 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 ...
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0answers
25 views

Bachelor thesis on Dijkgraaf Witten theory [on hold]

I am a Bachelor student with an interest in mathematical physics, and I want to write my bachelor thesis next year September. Since I am great fan of Robbert Dijkgraaf (as fellow Dutchman), I wanted ...
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0answers
65 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 $$ ...
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0answers
56 views

Wat would happen if I choose 1 = 0 when i make a field in algebra? [closed]

What would happen if I choose 1 = 0 when I make a field in algebra ? I mean $1$ is the neutral element for $\times$ and $0$ is the neutral element for $+$. So, what would happen if they are the same ...
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0answers
53 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 ...
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0answers
13 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 ...
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1answer
31 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 ...
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0answers
24 views

Multidimensional Quartic Equations [closed]

(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.) I know for ...
1
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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 ...
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0answers
58 views

Can’t we use ‘vector product’ to find the angle between two vectors? [migrated]

There are two vectors : $A = (\hat i + j + k)$ and $B = (\hat i - \hat j - \hat j)$, where $\hat i$, $\hat j$, and $\hat k$ are unit vectors along $x$, $y$, and $z$ axis respectively. We have to find ...
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0answers
26 views

Intuition for orientation of tri-vectors in geometric algebra [migrated]

I am learning geometric algebra from the MacDonald textbook and it states that the outer product is associative. Letting $\bf{u}$, $\bf{v}$, and $\bf{w}$ be vectors $$\bf{u} \wedge \bf{v} \wedge \bf{...
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0answers
68 views

Derivation of $\frac{\cos(\theta)dA}{r^2} = d\omega$ [closed]

Note: I asked the same question on the mathematics stackexchange, but was advised to ask it here. It also seems to arise quite often in physics. I've been looking for a (formal) derivation of the ...
5
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2answers
122 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 ...
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0answers
10 views

General distributional solution of the Airy Equation [migrated]

How can I prove that the Airy equation $$ \frac{d^2u}{dx^2}-xu = 0 $$ has at least two linear independent solutions?
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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 ...
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2answers
72 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 ...
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1answer
22 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
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0answers
46 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 ...
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0answers
27 views

What is the simplest way of getting the solid angle $\Omega_d$ in a space of $d$ dimensions? [migrated]

It is known that the solid angle in a flat space of $d$ dimensions ($d = 2 n$ or $d = 2 n + 1$) is given by these formulae: \begin{align}\tag{1} \Omega_{2 n} &= \frac{1}{(n - 1)!} \, 2 \pi^n, \...
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2answers
44 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 ...
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1answer
32 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 ...
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0answers
48 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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2answers
71 views

Dispersion Relations in Particle Physics [closed]

Please tell me how to get the identity(2) in this image
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2answers
132 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 ...
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1answer
52 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 $O(N)$?
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1answer
118 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
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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
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1answer
45 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
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1answer
19 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
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0answers
62 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
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0answers
74 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
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2answers
170 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
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1answer
87 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
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1answer
139 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 -...
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1answer
46 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 ...
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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 ...
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1answer
171 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 ...
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0answers
25 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 ...
0
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1answer
95 views

Statics problem: Finding resultant force angle measured from positive x-axis

I have this diagram: And I have done these calculations: $$R_x=-20sin(30)+30cos(35)+80cos(45)=71.14 \; lb$$ $$R_y=20cos(30)+30sin(35)-80sin(45)=-22.04 \; lb$$ The magnitude of this resultant force is ...
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1answer
121 views

Partial deritative of $\partial_V(PV)_T$ with $PV=nRT$

The question arised from thermodynmaics. Suppose $n,R$ are positive constants, and $P,V,T$ are all positive. From $TdS=dE+PdV$, one may obtain $T\partial_V(S)_T=\partial_V(E)_T+P$ where $\partial_V()...
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3answers
47 views

What is the significance of the second derivative of a function? [duplicate]

Basically, I just want to know the significance of the 2nd derivative of a function, or what does it tell us.
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0answers
30 views

Definition of Alternating $(k,0)$- and $(k,l)$-tensors

I know that one can define the alternating subspace of $(0,l)$-tensors in a straightforward way. These are the renowned $l$-forms. However, I have been searching in the literature for a definition of ...
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0answers
43 views

Best multivariable calculus books that covers partial derivative and multiple integrals …etc [duplicate]

all that I want is some books that cover partial derivative and multiple integrals, gradient, curl and divergence in a way that doesn't leave anything without saying why are we doing it in this way ...
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0answers
34 views

Physical Complex Space [closed]

I think if there is a system of coordinates consisted of real number, there is also a system of coordinates consisted of imaginary number. But this system is not a complex coordinate. It is only ...
3
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2answers
82 views

What's wrong with the following way to calculate mean lifetime from half-life?

So I understand that half-life $T_{1/2}$ is the time for the amount $N(0)$ to reduce by half. Basically, $$N(t)=N(0)2^{-t/T_{1/2}} $$ My question is that why can't I use this to directly pull out the ...
3
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2answers
211 views

Why might Roger Penrose argue that Godel's incompleteness theorem(s) suggest that consciousness is non-algorithmic?

This past March, when I called Penrose in Oxford, he explained that his interest in consciousness goes back to his discovery of Gödel’s incompleteness theorem while he was a graduate student at ...
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1answer
46 views

Can kinetic energy and potential energy or other similar quantities be considered multivariable functions?

We know that kinetic energy is mathematically represented as $$E_k = \frac{1}{2} m v^2$$ Similarly, potential energy is defined as $$E_p = mg\Delta x$$ Considering these mechanical quantities in a ...
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1answer
205 views

Legendre Transformation [closed]

Can someone explain how the Legendre transformation for multivariable functions work? I have been trying to find Legendre transformation for a function like $$F(x, y) = x^{2}+y^{2}+xy.$$ But I don't ...
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0answers
51 views

Stationary solutions: Fokker-Planck

I've a question about the stationary solutions of the FP equation. I know that for a differential stochastic equation like $$\frac{dx}{dt} = a(x) + \sqrt{2c}\eta $$ the FP equation is: $$\frac{\...