# Tagged Questions

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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### Objects in Physics as a mathematician would see them

I'm a mathematician with hardly any knowledge of physics. Before I start reading volumes of physics books, I have a few questions that have been bugging me and that will help me start reading physics. ...
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### 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 ...
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### Experimental Hopf fibrations

Recently I read a paper where the authors experimentally constructed a Hopf fibration - that is, they created a quantum system where the nematic vector field of the system had a non-zero Hopf ...
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### How deep can my knowledge of particle physics go without the maths?

By no means do I have the mathematical background to understand most of the math used in elementary particle physics. My current knowledge is of all the elementary particles and how they interact ...
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### 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 ...
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### Number of dimensions in string theory and possible link with number theory

This question has led me to ask somewhat a more specific question. I have read somewhere about a coincidence. Numbers of the form $8k + 2$ appears to be relevant for string theory. For k = 0 one gets ...
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### Is it possible for a physical object to have a irrational length?

Suppose I have a caliper that is infinitely precise. Also suppose that this caliper returns not a number, but rather whether the precise length is rational or irrational. If I were to use this ...
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### 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 ...
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### 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 ...
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### Are the solutions in radicals of cubic and quartic of any use in physics?

We all know that there are analytic formulae to solve quadratic, cubic and quartic polynomial equations. But it seems to me that the only solution that widely used is physics is the solution of ...
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### 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 ...
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### 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 ...
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### 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 $x^x$?
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### Uniqueness of Helmholtz decomposition?

Helmholtz theorem states that given a smooth vector field $\pmb{H}$, there are a scalar field $\phi$ and a vector field $\pmb{G}$ such that $$\pmb{H}=\pmb{\nabla} \phi +\pmb{\nabla} \times \pmb{G},$$ ...
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### 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 ...
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### Mathematical physics text with plenty of applications

I'm looking for texts on mathematical physics. I've seen various other threads, but the texts recommended in those threads were mathematical methods of theoretical physics texts, that is to say those ...
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### Why are three parameters required to express rotation in 3 dimension?

We know that in spherical coordinates angle $\theta$ and $\phi$ (two angles)are enough to express three dimensional rotation of matrix. But to express rotation mathematically as a transformation ...
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### 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 ...
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### 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}}...
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### What is a antiunitary operator?

In field theory one can define a time reversal operator T such that $T^{-1} \phi (x) T = \phi (\mathcal T x)$. It is then proved that T must be antiunitary: $T^{-1} i T = -i$. How is this equation ...
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### 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 ...
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### 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 ...
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### 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.
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### Meaning of integral signs in classical physics

When I began studying physics, by myself, on a universitary textbook, F.J. Keller, W.E. Gettys , M.J. Skove, Physics, about one year ago, I believed that all the integrals that I was going to find in ...
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### 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 ...
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### Is there a physical motivation to study finite fields?

Clearly finite groups are of immense value in physics and these are also substructures of fields. However I never came across any computations involving finite fields at university and so I never ...
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### 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 ...
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### 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 ...
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### For a theoretical (not mathematical) physicist, is there a need to learn pure mathematics?

For a theoretical physicist (not a mathematical physicist), is there a need to learn pure mathematics ?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 (v1+v2)...
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### 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 ...
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### 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 ...
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### 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 video,...
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### Combinatorial sum in a problem with a Fermi gas

I'm solving a problem involving a Fermi gas. There is a specific sum I cannot figure my way around. A set of equidistant levels, indexed by $m=0,1,2 \ldots$, is populated by spinless fermions with ...
### 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 ...