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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2
votes
4answers
273 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 ...
17
votes
4answers
858 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 ...
5
votes
4answers
328 views

Kähler and complex manifolds

I was wondering if anyone knows any good references concerning Kähler manifolds and complex manifolds? I am studying supergravity theories and for the simplest $\mathcal{N}=1$ supergravity we will get ...
3
votes
2answers
4k 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
624 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 ...
1
vote
0answers
49 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
380 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
49 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
427 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
498 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
259 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
253 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 ...
1
vote
3answers
412 views

Can we construct Axiomatic system of physical laws?

If we construct axiomatic system of physical laws that are independent one another as in axioms in mathematics, what should they be? Can there be such a finite system of physical laws that can explain ...
4
votes
1answer
114 views

Metric of a manifold foliated by maximally symmetric submanifold

I am reading the last chapter (Schwarzchild solution and Black Holes) of Sean Caroll's GR notes (http://arxiv.org/abs/gr-qc/9712019). While talking about spherical symmetry, he says how the ...
12
votes
4answers
959 views

What happened with Hilbert's sixth problem (the axiomatization of physics) after Gödel's work?

I'll write the question but I'm not fully confident of the premises I'm making here. I'm sorry if my proposal is too silly. Hilbert's sixth problem consisted roughly about finding axioms for physics ...
0
votes
2answers
162 views

Function with poles/singularities; Polynomial approximant has no poles

I don't know if i should ask this question or if it makes too much sense. My knowledge of this topic is quite incomplete, so please bear through with me. Any insights are appreciated. A function ...
7
votes
1answer
148 views

Are there cases in which we should consider tensors as equivalence classes?

Usually in texts about Physics that uses tensors defines them as multilinear maps. So if $V$ is a vector space over the field $F$, a tensor is a multilinear mapping: $$T:V\times\cdots\times V\times ...
7
votes
2answers
1k views

How important is mathematical proof in physics?

How important are proofs in physics? If something is mathematically proven to follow from something we know is true, does it still require experimental verification? Are there examples of things that ...
0
votes
1answer
115 views

The physical interpretation of limit of ratio of two functions

Imagine we have two different differentiable functions $f(t)$ and $g(t)$ where $t$ generally represents the time, if there exists the following limit as $$ \lim\limits_{t\rightarrow \infty } \frac{\| ...
4
votes
2answers
690 views

Normalization of the path integral

When one defines the path integral propagator, there is the need to normalize the propagator (since it would give you a probability density). There are two formulas which are used. 1) Original ...
2
votes
0answers
196 views

Modeling Syringes e.g. with the ideal gas law

Gentlemen I have a similar yet very practical problem that might provide further insight. I'm trying to model a moving plunger in a syringe (something like a piston in a cylinder). At time zero the ...
1
vote
2answers
2k views

What Is The Difference Between The Maths That Physicists Use And The Maths On A Typical Mathematics Degree [closed]

Cross-posted to Math.SE here. Physicists are widely respected for using and sometimes even inventing mathematics yet physicists study Physics which is a subject in its own right. So surely someone ...
2
votes
2answers
156 views

How to learn the wavelet transform?

Is there any good literature if I want to learn the wavelet transform? Especially my project is related with marine electromagnetism?
1
vote
0answers
48 views

Prequisite for the Feynman lectures? [duplicate]

It obviously requires single- and multi-variable calculus and linear algebra, but what else? And where do you suggest to get that background from?this isn't a duplicate because I'm for the math needed ...
2
votes
4answers
3k views

Necessary condition for square integrable functions?

I'm studying Quantum Mechanics and I came across this which I don't quite understand: For a vector space of functions $f(x)$ to be square integrable (i.e $\int{|f(x)|^2dx < \infty)}$, the necessary ...
2
votes
0answers
137 views

On “the geometry of free fall and light propagation” paper by Ehlers

In the paper The geometry of free fall and light propagation by Ehlers and his colleagues (Gen. Relativ. Gravit. 44 no. 6, pp. 1587–1609 (2012)), I reach to an axiom which says: There exists a ...
0
votes
0answers
63 views

Books for learning Mathematics in Physics? [duplicate]

Currently I'm doing Advanced Classical Mechanics courses. I'm finding it hard to understand due to the lack of knowledge in linear algebra, multi variable calculus and other chapters. Can anyone ...
20
votes
7answers
1k views

Tensor Operators

Motivation. I was recently reviewing the section 3.10 in Sakurai's quantum mechanics in which he discusses tensor operators, and I was left desiring a more mathematically general/precise discussion. ...
0
votes
0answers
83 views

Current density in phase space

I have a question which arises from looking at the impact free Boltzmann equation. Let $(\vec{x},\vec{v})$ be a vector in our phase space $\Gamma^N = \mathbb{R}^{6N}$. The dynamics of a state are ...
3
votes
2answers
471 views

Tensor Product of Hilbert spaces

This question is regarding a definition of Tensor product of Hilbert spaces that I found in Wald's book on QFT in curved space time. Let's first get some notation straight. Let $(V,+,*)$ denote a set ...
4
votes
3answers
1k views

Direct Sum of Hilbert spaces

I am a physicist who is not that well-versed in mathematical rigour (a shame, I know! But I'm working on it.) In Wald's book on QFT in Curved spacetimes, I found the following definitions of the ...
1
vote
0answers
104 views

Periodic sequence with exponentially increasing period?

I have to develop a physical model for a certain type of biological oscillation that can be built upon periodic sequences. From earlier questions I know that any periodic sequence (containing $0$s ...
7
votes
2answers
2k views

Differences between symmetric, Hermitian, self-adjoint, and essentially self-adjoint operators

I am a physicist. I always heard physicists used the terminology "symmetric", "Hermitian", "self-adjoint", and "essentially self-adjoint" operators interchangeably. Actually what is the difference ...
0
votes
1answer
154 views

Mathematics for Statistical Mechanics

I am studying Statistical Mechanics and Thermodynamics from a book that i am not sure who has written it, because of its cover is not present. There is a section that i can not understand: ...
1
vote
0answers
47 views

Ascertaining a mathematical equality to derive a partition function

we have an equation like this: $$\mathcal N(x)=\sum_{q=1}^\infty (\psi(x,q) \log(q)) \qquad (1)$$ while $\psi(x)$ is the function for some oscillations (may contain complex part), $x\in \Bbb R$ and ...
3
votes
2answers
455 views

Finite velocity at infinite distance

If an object were launched exactly at escape velocity it would have zero velocity at infinity. But what if we launch an identical objects at greater than escape velocity? Apparently it will have a ...
1
vote
0answers
78 views

Applications of a certain wave equation in Physics? [closed]

I am doing research in the field of number theory and as part of this looking for correspondencies to other discilines and particularly physics. I am searching for examples in physics where the ...
2
votes
1answer
495 views

Eigenvectors of a 4D rotation, and their interpretation

Let us define a 4D rotation by using two unit quaternions: $$\mathring{q}_l=\frac{a+ib+jc+kd}{\left|a+ib+jc+kd\right|}$$ and $$\mathring{q}_r=\frac{e+ib+jc+kd}{\left|e+ib+jc+kd\right|}.$$ They differ ...
1
vote
4answers
484 views

How can the big bang occur mathematically?

As we know time began with the big bang. Before that there was no time, no laws, nothing. Mathematically how can an event take place when no time passes by? How did the big bang took place when there ...
9
votes
6answers
855 views

In coordinate-free relativity, how do we define a vector?

Relativity can be developed without coordinates: Laurent 1994 (SR), Winitzski 2007 (GR). I would normally define a vector by its transformation properties: it's something whose components change ...
4
votes
2answers
156 views

Expanding two-variable function $f(x,y)$ over the complete sets $\{ g_{i}(x) \}$ and $\{ h_{j}(y) \}$

Quite often (see, for example, this PDF, 50 KB) when discussing the Born-Oppenheimer approximation the following assertion is made: any well-behaved function of two independent variables $f(x,y)$ can ...
-3
votes
2answers
124 views

Why is $r'/r^2 = -1/r$? [closed]

If $r=r(t)$, why is $\frac{r'(t)}{(r(t))^2}$ = $\frac{1}{r(t)}$ where $'$ denotes the derivative? I saw it in a lecture. Can you please explain?
-1
votes
2answers
312 views

Is there any phenomenon in physics which is sensitive to irrational numbers?

We can measure only rational numbers by our scale. Here is an example where irrational numbers does makes sense. If so then this question may have some theoretical importance. Is irrational numbers ...
4
votes
1answer
245 views

Does nature tetrate?

We see addition, multiplication and exponentiation in the natural formulae that make up physics. However, do we ever see tetration (repeated exponentiation) or higher hyper-operators in nature? ...
5
votes
2answers
297 views

Integer physics

Are there interesting (aspects of) problems in modern physics that can be expressed solely in terms of integer numbers? Bonus points for quantum mechanics.
2
votes
1answer
282 views

Spin(n) group SO(n) relation

Is it correct to state that the elements of Spin(n) fulfill a Clifford algebra and that the Lie group generators of Spin(n) is given by the commutator of the elements? If not, then what is the ...
1
vote
2answers
135 views

Suggestions on a particular arXiv publication on math needed for theoretical physicists [closed]

I'm going to start my PhD in a year and I'll be taking a gap year doing other stuff. But I also wanted to fill in the gaps in my math knowledge and I came across an arXiv publication called ...
14
votes
1answer
3k views

Equation describing magnetic hysteresis

So when you're looking at B-H curves for ferromagnetic substances, you often see these magnetic hysteresis curves, which occur, I gather, largely because of domain formation which has some reversible ...
0
votes
1answer
200 views

Universal Sequence and relationship of mathematics and reality [closed]

In "The Special and General Theory of Relativity" Einstein says: How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably ...
1
vote
2answers
236 views

Studying the logical structure of physics as a mathematical object per se? [closed]

I was wondering is there a branch of mathematical physics which studies the underlying logical structure of physics as a mathematical object per se? Let me explain what I mean by that. I'm ...