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 ...

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0answers
10 views

Proof from Calculus 1 [migrated]

Last days, from going into a website of the university of Pisa, I found an exercise given in the previous exams, in 1999. The problem was like: Given a continuous function f in R, and which ...
12
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4answers
580 views

Curvature of Hilbert space

That may appear as a dumb question, but: Does Hilbert space have curvature, or is it a flat space? How and why?
5
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1answer
173 views

Recent missed opportunities à la Freeman Dyson

There is an excellent paper by Freeman Dyson from 1972 (here) and therein the author cites old talks by Hilbert (here) and Minkowski (chapter 2 here) speaking about similar topics, namely how ...
0
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0answers
29 views

What is the minimum math level required to comprehend general relativity? [duplicate]

I am currently working on a B.S. In chemistry and only need to go up to Calculus II, though I like to dabble in physics. What other math classes could I take to gain greater understanding of higher ...
0
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0answers
4 views

Minima and maxima of a three variable function [on hold]

I have a three variable function $f(x,y,z)$ and I want to find its minima and maxima. I found its critical points and at one of its critical point, Hessian matrix look like $$ \begin{equation} H = \...
2
votes
2answers
119 views

Physics without math [on hold]

If anybody could imagine an advanced civilization with advanced knowledge of the universe(s) but without a mathematical language, how would they use their knowledge? How could it be possible to ...
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0answers
76 views

Physics Culture and the Attitude Towards Pure Math [closed]

To preface my question, I think it's important that I explain my experience studying both physics and pure math at the university level. I am American (as I'm sure education in different countries ...
13
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3answers
691 views

Infinite grid of planets with Newtonian gravity

Assuming only Newtonian gravity, suppose that the universe consists of an infinite number of uniform planets, uniformly distributed in a two-dimensional grid infinite in both directions and not moving ...
2
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1answer
201 views

Description of charged sphere with Heaviside function in cylindrical coordinates

I need to describe density of charge of uniformly charged sphere (radius R, total charge Q, position of centre (0,0,0)) with Dirac delta function and Heaviside step function. The hard part is to ...
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2answers
44 views

General Approach and Intuition to Calculus based problems in Physics [closed]

I've done a calculus-based course in Mechanics, Electromagnetism and at the moment I'm studying Strengths of Materials. Time and again, one is faced with problems where Integration is used to sum up ...
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1answer
88 views

What kind mathematical Transformation is this?

$$\int f(\alpha)e^{\alpha^*y-z|\alpha|^2}\pi^{-1}~\mathrm d^2\alpha~=~z^{-1}f(z^{-1}y)$$ I am doing the problem of finding Wigner function for fock states given by the exercise problem from ...
0
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1answer
27 views

How to visualize this setup for deriving $\frac {dM}{dt}$ while water is evaporating

Establish a minuscule area dA on the interface and establish two angular coordinates. We measure the polar angle θ with respect to a line drawn perpendicular to dA and the azimuthal angle φ with ...
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4answers
1k views

Does the axiom of choice appear to be “true” in the context of physics?

I have been wondering about the axiom of choice and how it relates to physics. In particular, I was wondering how many (if any) experimentally-verified physical theories require axiom of choice (or ...
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1answer
19 views

Why do proportionality constants come on only one side?

We know that voltage is directly proportional to current. Then if we change proportionality to equality, we get $V=IR$. Why not $I=RV$??
3
votes
1answer
134 views

Is it possible to build a logical theory in QM based on quantum logic? [closed]

Quantum Probabilities as Bayesian Probability, Quantum probabilities as degrees of belief Above are two articles about quantum Bayesianism. I don't know why quantum Bayesianism use some results from ...
0
votes
1answer
24 views

Is it correct to say that the constant of proportionality is proportional to the quantity itself?

So for instance, according to Newtons Law of cooling the rate of cooling is proportional to the temperature difference between the object and its surroundings. Mathematically $$\frac{dT}{dt}=-k(T-T_s)$...
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0answers
61 views

How to Solve this Integral

I am currently doing a problem in Quantum optics, specifically the problem of finding Wigner Function for Number states or Fock states. I am actually did the problem in a different way and found that ...
1
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1answer
110 views

Functional Analysis for Quantum Mechnanics [duplicate]

I have completed three sequences of courses in QM, and I'm very much eager to to do the functional analysis of QM on my own in my spare time. Can someone suggest some books? I like books with ...
0
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0answers
22 views

Spivak for a soon to be undergrad. physics student [duplicate]

I'll soon start my undergrad. studies in physics and because of that I picked up Spivak's Calculus a while ago to get a solid foundation in single-variable calculus before I start my studies. However, ...
0
votes
1answer
65 views

Use of infinitesimals in physics [duplicate]

I want to ask about infinitesimals and non-standard analysis. In physics we always use $\mathrm dx,~\mathrm dv,~\mathrm dt$ etc. as infinitesimal quantities. When we deduce equations in physics, when ...
4
votes
1answer
3k views

Spherical wave as sum of plane waves

How can we do this computation? $\iiint_{R^3} \frac{e^{ik'r}}{r} e^{ik_1x+k_2y+k_3z}dx dy dz$ where $r=\sqrt{x^2+y^2+z^2}$ ? I think we must use distributions... Physically, it's equivalent to ...
3
votes
1answer
44 views

Derivative with respect to a difference of independent variables

I am dealing with an equation from nonlinear acoustics (Khokhlova-Zabolotskaya-Kuznetsov equation) where a strange term (for me as a mathematician) is used. The equation looks like this $$ \frac{\...
0
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0answers
23 views

Mathieu equation nonstable solutions

This israther mathematical question, but it is connected with some physics. Let's have Mathieu equation: $$ \tag 1 y''(t)+ (a -2q\cos(2t))y(t) = 0 $$ Suppose domain of parameters $a, q$ values, where $...
12
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2answers
1k views

Unfamiliar Notation in Sakurai

In chapter 5 section 9 of Sakurai, 2nd edition, he uses some notation that I am unfamiliar with. This may be suited for Math.se but I figured it could be peculiar physicist notation. Anyways it is ...
1
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0answers
56 views

How to calculate the contour integration with branch point? [closed]

The question come from a Mutusbara Sum like this $${ \sum _{ { z=i\omega }_{ n } } { \frac { -\alpha E\pi }{ 4{ z }^{ 3 }\sqrt { -\alpha -z } } } }$$ it equal a contour integral around Imaginary ...
0
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0answers
51 views

What knowledge do I need to learn Quantum Physics? [duplicate]

I have a quick question. What prior knowledge do I need to learn and understand quantum physics. For example, what type of math do I need to know, what level of physics, etc.
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0answers
46 views

What is a good mathematical introduction to QFT [duplicate]

I've noticed that, any time I try to pick up Peskin and Schroeder, the main stumbling block it the leap in mathematical constructs from QM. Is there a good textbook that could teach me some of the ...
59
votes
11answers
12k views

Quantum Field Theory from a mathematical point of view

I'm a student of mathematics with not much background in physics. I'm interested in learning Quantum field theory from a mathematical point of view. Are there any good books or other reference ...
2
votes
2answers
107 views

Is multiplication in physics purely mathematical or is there a physical explanation to it?

Here is what I mean: We always use mathematics in physics, which is pretty powerful, but I still need to ask whether multiplication in physics has a better explanation to what I already think. For ...
0
votes
1answer
74 views

Exact solution of Qubit Decoherence using Transfer Matrix

I'm going through a particular paper on decoherence: Exact Solution of Qubit Decoherence models by a transfer matrix method I'm having trouble understanding a particular step in the mathematics ...
4
votes
1answer
103 views

Integrating elements of a Lie group with respect to parameters of the corresponding Lie algebra

I am working with an operator $\textbf{M}$ that is represented by the Lie group SO(1,3), thus it can be written as, $$ \textbf{M} = \exp{\textbf{L}} $$ where, $$ \textbf{L} = \begin{bmatrix} 0&a&...
1
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0answers
40 views

Relevance of pure mathematics vs statistics to physics [closed]

For someone currently studying physics, with an interest in experimental physics, would pure mathematics or statistics be more relevant?
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9answers
2k views

How to interpret the units of the dot or cross product of two vectors?

Suppose I have two vectors $a=\left(1,2,3\right)$ and $b=\left(4,5,6\right)$, both in meters. If I take their dot product with the algebraic definition, I get this: $$a \cdot b = 1\mathrm m \cdot 4\...
5
votes
0answers
80 views

Mutual $E$ force due to charged coaxial rings [closed]

I found the following question in a good physics book I was solving and although this is a computer problem, I wonder if it can be done without using computers. $Q.$ Find the force of attraction ...
1
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0answers
44 views

Can someone help me to do the math? [duplicate]

This might seems off topic or something, but I am a middle school student and i'm really into Quantum Field Theory and String theory and every video on youtube or article on the internet shows only ...
1
vote
1answer
51 views

Book to study Dirac delta function from a physics point of view [duplicate]

I am a beginning physics graduate student. I am often bewildered by the strange properties of the Dirac delta function such as: $\delta (a x)= \frac{1}{a} \delta (x)$ The derivative of $\delta (x)$ ...
13
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3answers
2k views

Book covering differential geometry and topology required for physics and applications

I am a physics undergrad, and interested to learn Topology so far as it has use in Physics. Currently I am trying to study Topological solitons but bogged down by some topological concepts. I am not ...
1
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0answers
22 views

Can you help me solve this using the current value Hamiltonian? [closed]

Okay, so I am getting a little stuck on this question, I will post it and then tell you how far I get. $$ max - \int_0^2 (x^2 + u^2)e^{-0.03t}dt\, $$ $$ x' = x-2u $$ $$ x(0) = 3 $$ $$ x(2)free $$ ...
0
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1answer
44 views

Assumptions in physics for Helmholtz decomposition

A version of the Helmholtz theorem says that, under opportune assumptions on the vector field $\boldsymbol{F}:\mathbb{R}^3\to\mathbb{R}^3$ and on $V\subset\mathbb{R}^3$ the following identity holds: $$...
27
votes
6answers
66k views

What is the physical significance of dot & cross product of vectors? Why is division not defined for vectors?

I get the physical significance of vector addition & subtraction. But I don't understand what do dot & cross products mean? More specifically, why is it that dot product of vectors $\vec{...
1
vote
2answers
1k views

What is the physical meaning of a dot product and a cross product of vectors? [duplicate]

My teacher told me that Vectors are quantities that behave like Displacements. Seen this way, the triangle law of vector addition simply means that to reach point C from point A, going from A to B &...
-1
votes
2answers
109 views

Disproving the mathematical universe hypothesis [closed]

The mathematical universe hypothesis is claimed by Lee Smolin to be falsifiable: [...] it is easy to disprove the mathematical-universe hypothesis. Simply exhibit one property of the natural world ...
5
votes
2answers
473 views

Proof of Ampère's law from the Biot-Savart law for tridimensional current distributions

Let us assume the validity of the Biot-Savart law for a tridimensional distribution of current:$$\mathbf{B}(\mathbf{x})=\frac{\mu_0}{4\pi}\int_V \mathbf{J}(\mathbf{y})\times\frac{\mathbf{x}-\mathbf{y}}...
2
votes
0answers
43 views

Seeking masters degree advice [closed]

I am graduating this semester with a bachelors in physics. My goal is to do theory in my graduate level course work. The problem I am in now is that I missed the deadline to take the physics GRE (I'm ...
1
vote
1answer
75 views

Why do people care about Mathieu groups and related things? (Something about monstrous moonshine)

Before I begin, let me say I don't know anything about what I am asking. This morning for somewhat random reasons I decided to google moonshine and related things. As it were I discovered my ignorance ...
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2answers
54 views

Can a laser beam be captured in prism?

is there a way to shoot a laser at a prism (or something) and have it glow when the laser hits it? I want to make a small box with a small hole in it. With the prism in the box, when the laser is ...
3
votes
1answer
82 views

Existence and Uniqueness of Newton's Laws

I'm reading Arnold's book on classical mechanics. This is kind of a dumb question, but I'm having problems understanding his explanation for existence and uniqueness of Newton's laws. On page $8$ he ...
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votes
2answers
63 views

What Are Logarithms? [closed]

I'm just starting out and have a limited area of mathematic study and have no idea how to do logarithms. I know that they're involved in physics and want to progress. Could someone help?
1
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0answers
54 views

Metric defining an sphere [closed]

I want to find for which cases this metric can define an sphere: $$\frac{1}{P^2}\left(\mathrm d\theta^2+\sin^2 \theta\; \mathrm d\phi^2\right)$$ where $P=\sin^2 \theta+K\cos^2 \theta$, with $K$ the ...
1
vote
3answers
89 views

Transition probability derivation

I have encountered this limit while learning time dependent perturbation and transition probability in Sakurai. How to show this limit? I tried to integrate around $x=0$ but didn't get anything useful?...