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75
votes
3answers
6k views

Has the Lie group E8 really been detected experimentally?

A few months ago there were several math talks about how the Lie group E8 had been detected in some physics experiment. I recently looked up the original paper where this was announced, "Quantum ...
70
votes
23answers
13k views

A soft introduction to physics for mathematicians who don't know the first thing about physics

There have been similar questions on mathoverflow, but the answers always gave some advanced introduction to the mathematics of quantum field theory, or string theory and so forth. While those may be ...
67
votes
2answers
104k views

Perfectly centered break of a perfectly aligned pool ball rack

Imagine the beginning of a game of pool, you have 16 balls, 15 of them in a triangle <| and 1 of them being the cue ball off to the left of that triangle. Imagine that the rack (the 15 balls in a ...
35
votes
6answers
6k views

Mathematical explanation of the failure to quantize gravity naively

One often hears in popular explanations of the failure to find a "Grand Unified Theory" that "Gravity goes off to infinity, but cutting off the edges gives us wrong answers", and other similar ...
23
votes
6answers
4k views

Explanations for mathematicians, about the falsifiability (or not) of string theory [closed]

Like many other mathematicians, I think string theory very attractive. This theory has wonderfully influenced many new topics in mathematics (I myself have worked on one of them), but it's not the ...
23
votes
3answers
2k views

How can simple physical “proofs” of mathematical facts be made rigorous?

Mark Levi's The Mathematical Mechanic is a book of examples of how physical reasoning can be used to solve mathematical problems; another couple of examples is in this blog post at Concrete Nonsense. ...
22
votes
11answers
2k views

What kind of Lagrangians can we have?

In any physics book I've read the Lagrangian is introuced as as a functional whose critical points govern the dynamics of the system. It is then usually shown that a finite collection of ...
20
votes
5answers
2k views

Is symplectic reduction interesting from a physical point of view?

Do you think that symplectic reduction (Marsden Weinstein reduction) is interesting from a physical point of view? If so, why? Does it give you some new physical insights? There are some possible ...
19
votes
6answers
2k views

Perpetuum Mobile

In 2 hours after posting this, I realized that preserving Liouville measure solves the problem completely. Sorry for disturbing... Construction of perpetuum mobile: Consider room with mirror walls ...
18
votes
5answers
3k views

Particle Physics and Representations of Groups

This question is asked from a point of complete ignorance of physics and the standard model. Every so often I hear that particles correspond to representations of certain Lie groups. For a person ...
16
votes
6answers
3k views

Angle Maximizing the Distance of a Projectile

It is well-known that to maximize the horizontal distance traveled by a projectile fired from the ground at a given speed, one should fire it at a $45^\circ$ angle. What's less-known, though not too ...
15
votes
3answers
473 views

An algebraic approach to the thermodynamic limit $N\rightarrow\infty$?

In physics one studies quite often the thermodynamic limit or what we call the $N\rightarrow \infty$ behavior of a system of $N\rightarrow\infty$ particles. This is of particular relevance in the ...
12
votes
9answers
2k views

Newton equations, second order equation and (im)possible motions

I am am currently studying Newtonian mechanics from a conceptional and axiomatic point of view. Now, if I am not mistaken, one (but surely not all) statement of Newtons second law about nature is, ...
11
votes
5answers
2k views

Flux through a Mobius strip

A friend of mine asked me what is the flux of the electric field (or any vector field like $$ \vec r=(x,y,z)\mapsto \frac{\vec r}{|r|^3} $$ where $|r|=(x^2+y^2+z^2)^{1/2}$) through a Mobius strip. It ...
11
votes
2answers
573 views

What do correlation functions compute in CFT?

I would like to understand what correlation functions compute in Conformal Field Theory in mathematics. Let me begin with basic definitions. We define a free boson field $\phi(z)$ as a formal power ...
10
votes
4answers
713 views

Can the equation of motion with friction be written as Euler-Lagrange equation, and does it have a quantum version?

My (non-expert) impression is that many physically important equations of motion can be obtained as Euler-Lagrange equations. For example in quantum fields theories and in quantum mechanics quantum ...
10
votes
2answers
832 views

Cone shaped solutions to wave equation

When I studied physics, we learned how to write down planar waves and spherical waves. But, when I turn on my flashlight, I see a cone of light. How can I see that there is a solution to the wave ...
10
votes
1answer
923 views

What is the “Physically Consistent” proper subset of arithmetic?

Suppose 1st-order arithmetic is inconsistent along with Voevodsky http://video.ias.edu/voevodsky-80th. It nevertheless remains true that when you have 2 apples and 2 apples, you have 4 apples. ...
9
votes
3answers
810 views

Is there an observer dependent mathematics? [closed]

Is there any field of mathematics that deals with the role of the observer? E.g., some formulation in which a set is changed, in some unspecified way, when it is observed? Or maybe some philosophy of ...
9
votes
1answer
975 views

Self-tightening knot

Is there a way, for some finite L>1, to tie two pieces of rope together, such that any finite force is not enough to pull them apart? The type of rope I have in mind is something like cylindrical ...
8
votes
4answers
2k views

Topology of black holes

I've asked this question of some physicist friends of mine and I've never gotten a satisfactory answer: What is topologically possible for a neighborhood of a black hole? To clarify, I'm curious about ...
8
votes
2answers
1k views

Derived Physics

Hello to all, This question will probably be closed down as being off-topic faster than one can say "string theory", but here it goes: I've noticed that the problems I'm working on -the structure of ...
8
votes
1answer
354 views

Dimensional regularization in odd dimensions

I am not quite sure that my question below is appropriate for this site, probably it should be addressed to the physical commutity. But I hope that some (mathematical) physicists do attend MO. I have ...
7
votes
1answer
1k views

What is the current state of the mathematics of Higgs fields?

Topical. I know there are good mathematical theories in which "Higgs" is used, in a geometrical sense. Would someone care to explain? To clarify, I'd like to know about Higgs bundles on Riemann ...
7
votes
3answers
1k views

Why do Physicists need unitary representation of Kac-Moody algebra?

My advisor mentioned to me that he talked to Witten last summer on representation theory, and Witten told him that unitary representations of Kac-Moody algebra are important to working physicists. But ...
7
votes
1answer
2k views

What is the meaning of symplectic structure? [closed]

Answers can come in mathematical, physical, and philosophical flavors. Edit: There seems to be a consensus that this question is not formulated well. I must respectfully disagree. My interest in the ...
7
votes
1answer
373 views

Two interacting bodies in an external field

Hope, MO is the right place for this question (if not so: where would you pose it?). Consider a two-body system in classical mechanics. As long as the interaction depends only on the distance of the ...
7
votes
1answer
357 views

A question on chiral rings and geometry of the vacuum bundle

I am reading "Mirror Symmetry" by Hori et al, and have a question on Chap.17 (Chiral rings and geometry of the vacuum bundle). On p.425 the authors say Consider the path-integral on the ...
6
votes
5answers
2k views

Optical methods for number theory?

I found a paper: 'A New Method of Finding the Distribution of Prime Number', saying We stack discs and annuluses with certain rules then turn on the light to illuminate. The projection of ...
6
votes
2answers
679 views

Quantum mechanics basics [closed]

Hello. I'm thinking about where does the basic quantum mechanics things comes from. I mean the forms of operators and a Shroedinger equation. The more intuitive explanation is better. To get forms of ...
6
votes
3answers
488 views

Literature for gauge field theory on the lattice in geometrical formulation

I have found an article by Huebschmann, Rudolph and Schmidt: http://www.springerlink.com/content/b8v216v0m8h16264/ about "A Gauge Model for Quantum Mechanics on a Stratified Space" and I am very ...
6
votes
1answer
234 views

Orbits for homogenous complex polynomials under unitary rotation of variables

Let's have two complex homogeneous polynomials of degree $k$: $f(z_1,\cdots,z_n)$ and $g(z_1,\cdots,z_n)$. We consider rotations of variables in the form of $\vec{z}' = U \vec{z}$, where $U\in SU(n)$. ...
5
votes
2answers
872 views

Homotopy $\pi_4(SU(2))=Z_2$

I am a physics student, recently I read a paper using Homotopy $\pi_4(SU(2))=Z_2$, I guess mathematicians have some visualization or explanation of this result. So I come here ask for help. ...
5
votes
2answers
965 views

Mathematical definition of running

This will be a tad hard to explain, so bear with me. Taking into account only the legs what would be an accurate definition of the position of the upper legs, lower legs and feet with respect to time? ...
5
votes
2answers
408 views

Permuting Racked Pool Balls with a Single Break

Given reasonable physical assumptions (on friction, collisions, etc.), would it be possible to "break" in a pool game such that when all the balls come to rest, the only difference is that the racked ...
5
votes
2answers
788 views

Singular K3 — mathematical meaning?

There's a very interesting text by Cumrun Vafa called Geometric Physics. Here I'm particularly interested in Chapter 4, where we take a Calabi-Yau manifold presented as a degenerating fibration: ...
4
votes
2answers
3k views

Something like mathoverflow in other sciences [closed]

Are the sites similar to mathoverflow in other sciences related to mathematics? statistics, computer science, physics, economics, etc? Let me explain what I mean by "similar": those are sites devoted ...
4
votes
1answer
456 views

Impact of LHC on math ? [closed]

LHC (Large Hadron Collider) "... remains one of the largest and most complex experimental facilities ever built". May be it is even the most complex project in humankind's history(?). Such projects ...
4
votes
2answers
146 views

Analytic solution of a system of linear, hyperbolic, first order, partial differential equations

In a try to solve a physical problem, I've faced a system of first-order partial differential equations of the form ...
4
votes
1answer
311 views

About using the character formula for $SO(2n)$.

I have known of the following equation for characters of a $SO(2n)$ representation with highest weights $(h_1,...,h_n)$ and for $(t_1,t_2,..,t_n,t_1^{-1},t_2^{-1},..,t_n^{-1})$ being the eigenvalues ...
3
votes
1answer
555 views

Which motion is exclusive in 3D or higher dimensions?

Hi guys, I have a simple question Linear movement can be found in 1D, 2D and 3D world objects Rotation can be found in 2D and 3D world objects. Now, are there any kind of motion can only be found ...
3
votes
2answers
1k views

Maxwell Stress Tensor and Equations in Mathematician's Language [closed]

In my language, a differential two-form on $\mathbb{R}^4$ (viewed as a differentiable manifold with coordinates $t,x,y,z$) is a differentiable choice at each point of an alternating bilinear function ...
3
votes
1answer
769 views

Is there an analogue of mathscinet for physics?

I've been looking recently at some papers in physics, from journals that are not listed in mathscinet. Is there is a similar database for physics, with reviews and citation links? I'd like to see ...
3
votes
1answer
670 views

Minimize Energy for Charge Distributions

I am considering [positive] charge distributions $\rho:M\rightarrow\mathbb{R}_+$ (nonnegative reals) with unit charge $\int_M\rho=1$ for convenience. Here $M$ is a nice-enough region, say a ...
3
votes
3answers
561 views

Best book for learning sensor fusion, specifically regarding IMU and GPS integration.

I have posted this in MathOverflow because the subject is primarily Math related. I have a requirement of building an Inertial Measurement Unit (IMU) from the following sensors: Accelerometer ...
3
votes
1answer
259 views

Prevalence of B-fields

I am wondering how B-fields, which are basic objects in Generalized Geometry, relate to the B-fields of Ben's question and the answers to it. In Generalized Geometry, the B-field is a (1,1)-form, and ...
3
votes
1answer
287 views

A particular contour integral

Mathoverflow, I'd like to carry out the following integral, $$f(t) = \int_{- \infty}^{\infty}\frac{-i\Omega e^{i \Omega t}}{1-\sqrt{-i\Omega}\coth(\sqrt{-i\Omega})} d\Omega.$$ Here's what I've ...
3
votes
1answer
129 views

Three body problem with point interactions

I've studied the HVZ theorem for the three body problem interacting with regular potentials. I'd like to extend this result to the three body problem with point interactions (delta potentials). Is ...
3
votes
1answer
230 views

Solvable models in quantum mechanics

Is there anyone who studied on the book "Solvable Models In Quantum Mechanics" by Albeverio? I don't succed in understanding the proof of page 116 about the eigenvalues of the Hamiltonian with point ...
3
votes
1answer
320 views

Path integrals for stochastic equations

Does there exist a rigorous mathematical proof for path integral representations given in the physics literature? See for example http://arxiv.org/abs/hep-ph/9912209v1 For imaginary time rigorous ...