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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10
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2answers
1k views

How should a theoretical physicist study maths? [duplicate]

Possible Duplicate: How should a physics student study mathematics? If some-one wants to do research in string theory for example, Would the Nakahara Topology, geometry and physics book and ...
-4
votes
4answers
159 views

Is the mathematical truth 1+1=2 analogous to the conservation of energy? [closed]

They seem to express the same concept in different fields.
3
votes
2answers
344 views

(Co)homology of the universe

In this post let $U$ be the universe considered as a manifold. From what I gather we don't really have any firm evidence whether the universe is closed or open. The evidence seems to point towards it ...
1
vote
1answer
202 views

Potential for charge distribution, finiteness

Consider a potential for charge distribution: $$v_H(\mathbf{r}) ~=~ \int \frac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|}d\mathbf{r'}$$ where $\rho(\mathbf{r'})$ is the charge density. This ...
1
vote
0answers
89 views

Division algebras $(\mathbb{R,C,H,O})$ and discrete symmetry [closed]

I once saw a statement about the relation between division algebra(which means you can define a division in this algebra, there is a theorem saying we only have 4 kinds of division algebra, real R, ...
10
votes
6answers
984 views

Is physics rigorous in the mathematical sense?

I am a student studying Mathematics with no prior knowledge of Physics whatsoever except for very simple equations. I would like to ask, due to my experience with Mathematics: Is there a set of ...
13
votes
4answers
612 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 ...
4
votes
1answer
150 views

The use of Hall algebras in physics

I asked the same question in mo. I think maybe here there are more physics guys to help me. I once read a statement (not memorized precisely) that a certain physics quantity between two states of ...
8
votes
0answers
509 views

String theory from a mathematical point of view

I have a great interest in the area of string theory, but since I am more focused on mathematics, I was wondering if there is any book out there that covers mathematical aspects of string theory. I ...
3
votes
1answer
302 views

Mathematical definitions in string theory

Does anyone know of a book that has mathematical definitions of a string, a $p$-brane, a $D$-brane and other related topics. All the books I have looked at don't have a precise definition and this is ...
3
votes
0answers
239 views

Integrals given by Landau [closed]

Discussion about Landau's "Theoretical Minimum" has already been posted here. Unfortunately I couldn't find much about some examples of questions he gave to students. There are three questions in the ...
4
votes
2answers
368 views

Quantum Mechanics in terms of *-algebras

I'm currently trying to find my way into the geometric description of Quantum Mechanics. I therefor started reading: Geometry of state spaces. In: Entanglement and Decoherence (A. Buchleitner et ...
2
votes
3answers
518 views

Mathematics for Quantum Mechanics [duplicate]

What math should I study if I want to get a basic understanding of quantum mechanics and especially to be able to use the Schrodinger's equation.
5
votes
4answers
2k views

How do you do an integral involving the derivative of a delta function?

I got an integral in solving Schrodinger equation with delta function potential. It looks like $$\int \frac{y(x)}{x} \frac{\mathrm{d}\delta(x-x_0)}{\mathrm{d}x}$$ I'm trying to solve this by ...
2
votes
1answer
226 views

Why is physical space equivalent to $\mathbb{R}^3$?

Why is physical space equivalent to $\mathbb{R}^3$, as opposed to e.g. $\mathbb{Q}^3$? I am trying to understand what would be the logical reasons behind our assumption that our physical space is ...
6
votes
5answers
639 views

What is the meaning of following expresion $C=\frac{\delta Q}{dT}$ mathematicly

Our professor raised the following question during our lecture in Statistical Physics (even so it's related to Thermodynamics): Many text books (even wikipedia) writes wrong expressions (from ...
4
votes
2answers
352 views

Sum total distance of electrons on a spherical surface

What is the sum total distance between every possible pair of point charges when there are n point charges on a spherical surface? All point charges can only and are located on the infinitesimal ...
7
votes
2answers
296 views

Quantum mechanics on Cantor set?

Has quantum mechanics been studied on highly singular and/or discrete spaces? The particular space that I have in mind is (usual) Cantor set. What is the right way to formulate QM of a particle on a ...
6
votes
7answers
1k views

Why are radians more natural than any other angle unit?

I'm convinced that radians are, at the very least, the most convenient unit for angles in mathematics and physics. In addition to this I suspect that they are the most fundamentally natural unit for ...
0
votes
2answers
72 views

What is the minimal set of expectation values I need in a statistical model?

At least if $\vec v$ is really only a one dimensional parameter, measuring all the moments $\langle v^n \rangle_f$ seems to give me all the information to compute $\langle A \rangle_f$ with $A(v)$ ...
3
votes
2answers
184 views

Mathematical problems with impact on physics [closed]

Are there any purely mathematical, unsolved questions, whose resolution would have (great, or concrete) impact on physics? Eg. it could almost surely tell us whether particle x exist or not, assuming ...
2
votes
0answers
197 views

How is the poincare conjecture(and perelman proof) helpful in studying the properties of the universe?

Can someone tell me how the poincare's famous conjecture or its proof by perelmen can be helpful in deciding some properties like the shape of the universe?
3
votes
4answers
706 views

Topology needed for Differential Geometry [duplicate]

I am a physics undergrad, and need to study differential geometry ASAP to supplement my studies on solitons and instantons. How much topology do I need to know. I know some basic concepts reading from ...
4
votes
3answers
363 views

shifting from mathematics to physics

I am a postgraduate in mathematics. I studied physics during my B.Sc.studies.I want to go for further studies in physics particularly in theoretical physics. I am in a job and cant afford regular ...
6
votes
2answers
803 views

Book covering 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 ...
3
votes
0answers
189 views

What are the topics of string theory that are comprehensible with only a mathematical background on Manifolds and Algebraic Topology?

What are the topics of string theory that are comprehensible with only a mathematical background on manifolds and algebraic topology? Also, I have read only the first four chapters in Peskin & ...
3
votes
1answer
329 views

How do I find the tensor components of all weights of a representation of $SU(3)$, e.g. the six dimensional representation $(2,0)$?

How do I find the corresponding tensor component $v^{ij}$ of the six dimensional representation of $SU(3)$ with Dynkin label $(2,0)$?
0
votes
1answer
212 views

Control system with equation C = A*x + B*dx/dt

This question came up in a computer science / robotics exam and I still don't know the solution for it. I figured out that it's classical mechanics related, so I thought this might be the best place ...
0
votes
1answer
187 views

Looking for a way to simplify a physics formula [closed]

I have the following physics formula: $$d = \frac{1}{2} at^2$$ where d is equal to half (at) squared where: d is distance a is acceleration t is time I need to simplify this to get the ...
2
votes
2answers
539 views

Coulomb potential energy functional derivative

I'm having problem understanding how to compute a functional derivative when it's involved more than one integral, such as the coulomb potential energy functional: $$ J[\rho] = \frac 12\int ...
7
votes
2answers
311 views

Advice on doing physics under the umbrella of mathematics and the converse

In the current scenario of research in QFT and string theory (and related mathematical topics), which of the following would an undergraduate student, like me, be advised to do and why if s/he is ...
0
votes
2answers
244 views

Is there a named unit that, when divided by 32, gives meters per second?

I am receiving unknown units of speed from another system. I must divide the value by 32 to get meters per second. What units do I use to refer to the values I'm receiving? Is there any such unit? Is ...
7
votes
3answers
2k views

A book on quantum mechanics supported by the high-level mathematics

I'm interested in quantum mechanics book that uses high level mathematics (not only the usual functional analysis and the theory of generalised functions but the theory of pseudodifferential operators ...
3
votes
4answers
315 views

How do I go from exponents to a formula?

This is a continuation of this question. http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-1/ skip this lecture to around 25:50. After doing ...
0
votes
1answer
105 views

Does one require calculus to work with uncertainities?

I'm very young so know no calculus whatsoever. I want to be able to calculate uncertainties for a Physics course I'm doing online, but I believe you need to have knowledge of differentials to do this ...
4
votes
1answer
313 views

Differentiating inside an integral sign

I'm reading John Taylor's Classical Mechanics book and I'm at the part where he's deriving the Euler-Lagrange equation. Here is the part of the derivation that I didn't follow: I don't get how ...
5
votes
0answers
496 views

Good theoretical physics introduction for 6 year old very advanced in math? [duplicate]

I think now is a good time to introduce my son to theoretical physics. He asks so many questions about the universe, black holes, gravity, atoms, molecules, light, etc. He's borderline obsessed with ...
1
vote
1answer
577 views

Bra space and adjoint vectors

If I'm not wrong, a bra, $ \langle \phi_n | $, can be thought as a linear functional that when applied to a ket vector, $| \phi_m \rangle$, returns a complex number; that is, the inner product it's a ...
7
votes
3answers
2k views

What math do I need for mathematical physics? In what manner should I learn math? [closed]

I'm a freshman undergraduate. I've got my sight on mathematical physics. I love math but I don't have the talent nor the inclination for purely abstract mathematics. I also love physics. The only ...
2
votes
0answers
260 views

A solvable model for the finite rectangular potential well with a bump in the middle

A well known example in quantum mechanics is that of a finite rectangular potential well with a rectangular bump in the middle. I guess this closely approximates the "umbrella" effect of the $NH_3$ ...
9
votes
4answers
1k views

What is the physical meaning of a “complete” Hilbert space in QM?

What does the word "complete" means from the physical point of view? I do not understand what it physically means to say that a Hilbert space is a complete vector space.
5
votes
6answers
2k views

How is gradient the maximum rate of change of a function?

Recently I read a book which described about gradient. It says $${\rm d}T~=~ \nabla T \cdot {\rm d}{\bf r},$$ and suddenly they concluded that $\nabla T$ is the maximum rate of change of $f(T)$ ...
0
votes
1answer
185 views

How to describe the inner curve of a crescent?

What is the equation which describes the inner circle of the crescent that a celestial body displays when view at an angle from its light source, as a function of the crescent-cycle period? For ...
30
votes
10answers
1k views

Readable books on advanced topics [closed]

I realise that there are already a few questions looking for general book recommendations, but the motivation and type of book I'm looking for here is a little different, so I hope you can indulge me. ...
3
votes
3answers
2k views

Why is the angle of a pendulum as a function of time a sine wave?

OK so I'm trying to understand why the angle of a pendulum as a function of time is a sine wave. I can't really find an explanation online and when I do find something partial there are certain ...
11
votes
3answers
620 views

Mathematical Physics Book Recommendation [duplicate]

Possible Duplicate: Best books for mathematical background? I want to learn contemporary mathematical physics, so that, for example, I can read Witten's latest paper without checking other ...
4
votes
2answers
389 views

Why model space with real numbers?

Are there any good papers discussing why we use $\mathbb{R}^{3}$as a model for space? More specifically are there any that explain why we don't use other number systems such as extensions of the real ...
30
votes
10answers
1k views

Examples of number theory showing up in physics

My question is very simple: Are there any interesting examples of number theory showing up unexpectedly in physics? This probably sounds like rather strange question, or rather like one of the ...
3
votes
2answers
151 views

Infinitesimal input, macroscopic output

I must admit that I never got well how physicists handle infinitesimal quantities, mainly because of my education as a mathematician. So the following lines (taken from the preface of Berezin and ...
2
votes
3answers
667 views

What does the differential of $d_s\sin(\theta) = m\lambda$ help us see, with respect to waves through diffraction gratings?

With respect to waves traveling through a diffraction grating, we have an equation like this one: $$d_s\sin(\theta) = m\lambda.$$ Where $d_s$ is the distance between slits in the grating, $\theta$ is ...