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13
votes
4answers
3k views

Is speed of light and sound rational or irrational in nature?

Just as circumference of circle will remain $\pi$ for unit diameter, no matter what standard unit we take, are the speeds of light and sound irrational or rational in nature ? I'm talking about ...
2
votes
1answer
47 views

What are the proper domains of the position and squared angular momentum operator?

I am looking at the position operator on a compact set $K \subset \mathbb{R}^n$ and the squared angular momentum operator (so essentially the Laplace-Beltrami operator where I just look at the angular ...
2
votes
0answers
31 views

Are there any applications of elementary number theory to science? [duplicate]

I've taken a class on elementary number theory (for fun), but now I wonder: was it at all useful to learn number theory for my future career in physics? More to the point, are there any applications ...
0
votes
1answer
47 views

Resources for theory of distributions (Generalized functions) for physicists

I am looking for tutorials, articles or books containing theory of distributions in context of mathematical physics. Please suggest.
0
votes
0answers
49 views

Are there any odd fields of mathematics with physics? [closed]

Every body knows that calculus,geometry,algebra,topology..etc are used in physics. But is there any fields of mathematics that are seemingly unrelated to physics ( like number theory ) that show any ...
1
vote
0answers
51 views

Is it possible to do a PhD in theoretical physics after a BSc in Mathematics [closed]

I would like to ask if it is useful to have a solid maths background (but only 2 courses of "general physics" and 2 of "mathematical physics") as BSc in order to be a successful researcher in ...
1
vote
0answers
52 views

Most useful maths for theoretical and mathematical physics [closed]

I am going to apply for a programme of mathematical and theoretical physics for graduate studies and I'm currently studying maths. What is a good area to do a thesis (that is to say, considerable ...
1
vote
0answers
77 views

mathematician or physicists [closed]

Mathematicians consider physicists as people who simply use mathematics as a tool but are in a way, let's say, inaccurate, as physicists tend to make assumptions a lot in their mathematics and ...
3
votes
0answers
48 views

Scalar product of torsional forms - how are the standard identities modified?

It is known that for any smooth, orientable, compact manifold $X$ without boundary and $\alpha \in \Omega^{r}(X), \beta \in \Omega^{r-1}(X)$ it holds \begin{equation} (d\beta,\alpha)= (\beta, ...
0
votes
0answers
9 views

What is a circle's area if its radius is $\pi$? [migrated]

The area of a circle equals $\pi r^2$. If a circle's radius is $\pi$, what is its area? I believe the answer is $\pi^3$, right?
2
votes
1answer
27 views

Taylor expansion of translated fields

First of all, I would like to say that I am somewhat new to four-vector notation. I have a function of a four-vector that I want to expand. $$ A_\mu (\mathbf{x} + \mathbf{x}_0) = A_\mu (\mathbf{x}) ...
2
votes
0answers
28 views

Book for multivariable calculus [duplicate]

Hi I want to start learning multi variable calculus specifically for learning electrodynamics. What are some good text books?
2
votes
1answer
134 views

Why are there equations in physics with factors of 2, 3 and 5, but there aren't any with factors of 7 or 11?

I noticed that there are a lot of equations in physics with factors of 2, 3 and 5 (either in the numerator or in the denominator), but there aren't any with factors of 7 or any prime number greater ...
2
votes
1answer
75 views

Basic maths theories for good understanding of the standard model [duplicate]

I want to know what mathematical theories I should be aware of for a deep understanding of the standard particles model.
0
votes
0answers
76 views

Dirac Delta function

Although I find it mathematically dubious, we said that $\Delta \frac{1}{r} = -4\pi \delta(r)$. Now, I was wondering is there a similar relation to the delta function if we look at $\Delta ...
2
votes
4answers
81 views

Infinite series of derivatives of position when starting from rest

Suppose you have an object with zero for the value of all the derivatives of position. In order to get the object moving you would need to increase the value of the velocity from zero to some finite ...
4
votes
1answer
113 views

Which is the role of Algebraic Geometry in String Theory? [closed]

Could someone sketch me what algebraic geometry has to do with string theory? Are there other mathematical disciplines that are interwoven with string theory? I'm aware of a similar question on ...
4
votes
1answer
269 views

What areas of physics depend on the sum $1 + 2 + 3 + 4 + 5 + 6+ 7+\ldots= -1/12$? [duplicate]

This youtube video from Numberphile, http://youtu.be/w-I6XTVZXww shows how the value is derived. In the video, one interviewee claims that "this result is used in many areas of physics". In the ...
4
votes
1answer
160 views

Did Maxwell invent the math to describe the ideas of electromagnetism?

Did he invent surface and line integrals, or did they already exist when he formulated his equations. If they did, already exist, how did they come about in pure math?
14
votes
8answers
2k views

Why are sine/cosine always used to describe oscillations?

What I am really asking is are there other functions that, like $\sin()$ and $\cos()$ are bounded from above and below, and periodic? If there are, why are they never used to describe oscillations in ...
0
votes
3answers
129 views

Good math books for physicists [duplicate]

In his first lesson (transcripted in "Tips on Physics"), Feynman talks about math for physicists in a very cool and practical way. And at the end of the section he talks something like "so the first ...
3
votes
1answer
87 views

References on $C^{*}$-algerbas, $W^{*}$-algebras and Quantum Theories

I would like to know some references regarding $C^{*}$ and $W^{*}$-algebras and quantum theories. I'm interested in concrete physical applications, models and problems. Here it is the list of ...
3
votes
1answer
121 views

A question about canonical transformation

I have posted this question in math.stackexchange before with no answer till now. It may be more suitable to post here. There is a problem in Arnold's Mathematical Methods of Classical Mechanics ...
8
votes
0answers
214 views

p-Adic String Theory and the String-orientation of Topological Modular Forms (tmf)

I am going to ask a question, at the end below, on whether anyone has tried to make more explicit what should be a close relation between p-adic string theory and the refinement of the superstring ...
2
votes
0answers
41 views

Is rigorous functional analysis useful for theoretical physics? [duplicate]

I'm an undergraduate physics without much quantum mechanics at all under my belt. I'm studying functional analysis, and I want to know whether or not this will be useful for me in theoretical physics ...
0
votes
1answer
33 views

A question about Hamiltonian phase flow

Show that if a one-parameter group of difeomorphisms of a symplectic manifold preserves the symplectic structure then it is a locally hamiltonian phase flow. Note that A locally hamiltonian ...
0
votes
0answers
28 views

Self-teaching physics recommendations? [duplicate]

I've been very interested in mathematics for a while now and, after being inspired by reading Feynman's biography, would also like to learn about physics. My mathematics background is fairly ...
5
votes
1answer
114 views

Where and how exactly does string theory and Q.E.D. use zeta function regularization?

In the video they mention it being used in many fields of physics inclusing String and QED theory. https://www.youtube.com/watch?v=w-I6XTVZXww But I remember reading somewhere that 1+2+3..=-1/12 is ...
2
votes
2answers
116 views

Absolute value in the argument of a logarithm

I am wondering how the author rationalizes the removal of absolute value bars around the quotient argument of a natural logarithm. My take on this is that the potential at point $b$ MUST be greater ...
0
votes
0answers
79 views

How simplify functional derivatives (in path integrals) with mathematica?

Are there any packages that can simplify functional derivatives in path integrals? For instance the expression (integrate over, $x,y,z,u,v,r,s$): ...
2
votes
0answers
87 views

Questions about closed forms and cycles

I read the section closed forms and cycles in Arnold's Mathematical Methods of Classical Mechanics (page 196-200), but the problems in this section is too difficult to solve in the way following the ...
0
votes
0answers
46 views

To all experienced theoretical physicists out there, what is the step by step process in your math education? [duplicate]

I am not doing a physics degree but an engineering degree but i am planning using my free time to self study all the math in preparing myself to self study subjects in theoretical physics. (I've ...
6
votes
1answer
107 views

Determining the Hodge numbers of some orbifold examples

I'm currently reading about complex geometry in order to get a feeling of how to determine the Hodge numbers, e.g. of certain orbifold constructions. Since I'm a physicist with no deeper mathematical ...
0
votes
0answers
24 views

Mathematics for physics resources [duplicate]

Looking for book suggestions. I have a good basic understanding of many mathematical concepts but I want to improve to a physicist level. This is mainly because I want to study atmospheric physics ...
3
votes
2answers
141 views

In what way are the Mathematical universe hypothesis and A New Kind of Science connected

The Mathematical universe hypothesis, mainly by Max Tegmark and A new Kind of Science, mainly by Stephen Wolfram both claim (as least as I understand it) that at its innermost core reality is ...
1
vote
4answers
422 views

What is fundamentally physically impossible?

Mathematical logic defines quite clearly what is true or false in math, and also that some theorems are impossible to prove. This resulted in some clear definitions of axioms set like Peano, ZF or ...
2
votes
4answers
169 views

Why does $E=\nabla\phi$ follow from $\nabla\times E=0$?

I understand that using one of Maxwell's equations, $$\vec{\nabla} \times \vec{E}(\vec{x})=0,$$ it can be said that $$\vec{E}(\vec{x})=-\vec \nabla \phi(\vec{x}).$$ However, I can't find or ...
0
votes
0answers
32 views

The sum of positive integers equals minus one twelfth [duplicate]

I was watching a lecture online from the american physicist Lawrence Krauss, when he made an off the cuff remark about the sum of all the positive integers being equal to one twelfth. My question is ...
15
votes
4answers
602 views

Hilbert, Gödel, and “God equations” - a 19th century lesson for 21st century physicists?

It seems there are a lot of respected physicists appearing on pop-sci programs (discovery channel, science channel, etc.) these days spreading the gospel of "we can know, we must know." Three ...
0
votes
0answers
42 views

Collapse of wave function

Can the collapse of a quantum mechanical state in general into one the eigenstates of an observable whenever its measurement is made written mathematically? If yes, how?
5
votes
4answers
174 views

Kähler and complex manifolds

I was woundering if anyone knows any good references about Kähler and complex manifolds? I'm studying supergravity theories and for the simplest $\mathcal{N}=1$ supergravity we'll get these. Now in ...
3
votes
2answers
3k views

How does the sum of the series “1 + 2 + 3 + 4 + 5 + 6…” to infinity = “-1/12”? [duplicate]

How does the sum of the series “1 + 2 + 3 + 4 + 5 + 6…” to infinity = “-1/12”, in the context of physics? I heard Lawrence Krauss say this once during a debate with Hamza Tzortzis ...
6
votes
2answers
438 views

Does the wave function always asymptotically approach zero?

I'm new to quantum physics (and to this site), so please bear with me. I know that quantum mechanics allows particles to appear in regions that are classically forbidden; for example, an electron ...
0
votes
0answers
42 views

Advice on beginning self learning physics from scratch [duplicate]

I am pursuing masters degree in computer applications. I have no formal Mathematics and Physics background but for masters degree entrance examination I have studied senior high school level ...
2
votes
1answer
194 views

A question about Fermi-Dirac Distribution function

It seems more like a mathematical question, about the property of Fermi-Dirac Distribution function $$f=\frac{1}{e^{(E-\mu)/k_BT}+1}$$ where $\mu$ is the chemical potential and $k_B$ is the Boltzmann ...
0
votes
0answers
46 views

Are there some websites for self learning of advanced mathematics? [duplicate]

Are there some websites for self learining of advanced mathematics? For example there is perimeterscholars for self study of theoretical physics, but I haven't found some good websites providing ...
0
votes
2answers
207 views

Math required for learning Lagrangian mechanics [duplicate]

How much knowledge of maths is required for learning Lagrangian mechanics? Also from where can I learn this math?
3
votes
1answer
196 views

Math needed for undergrad Statistical Mechanics/Thermal Physics

A professor recommended me to take a course on Statistical Physics as preparation for agent-based computing in social sciences. Now I have no experience in physics beyond basic highschool, and ...
7
votes
1answer
245 views

Is there any usage of $x^x$ in physics? [closed]

I am so excited about the function: $x^x$. I would like to know if there is any usage in the physics world of this function. Is there any formula that uses $x^x$?
3
votes
1answer
193 views

Etale bundles and sheaves

Before answering, please see our policy on resource recommendation questions. Please try to give substantial answers that detail the style, content, and prerequisites of the book or paper (or ...