Questions tagged [physics]
For questions about mathematical problems arising from physics, the natural science studying general properties of matter, radiation and energy.
189
questions
150
votes
26
answers
47k
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 ...
105
votes
3
answers
9k
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 ...
- 20.4k
95
votes
2
answers
114k
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 ...
- 989
70
votes
10
answers
11k
views
The Planck constant for mathematicians
The questions
Q1. What are simple ways to think mathematically about the physical meanings of the Planck constant?
Q2. How does the Planck constant appear in mathematics of quantum mechanics? In ...
- 24.2k
52
votes
6
answers
13k
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 ...
52
votes
5
answers
4k
views
When exactly and why did matrix multiplication become a part of the undergraduate curriculum?
The story about Heisenberg inventing matrices and matrix multiplication in 1925 is very well known and well documented. A few weeks later, Born and Jordan read this work and recognized matrix ...
- 88.9k
43
votes
7
answers
13k
views
Number theory and physics
I was following some lectures by Edward Frenkel about Langlands correspondence. He was describing some analogies between number theory and theoretical physics (Mirror symmetry). At some point ( my ...
- 1,603
38
votes
4
answers
6k
views
On critical reviews of Hawking's lecture "Gödel and the end of the universe"
The search for a neat Theory of Everything (ToE) which unifies the entire set of fundamental forces of the universe (as well as the rules which govern dark energy, dark matter and anti-matter realms) ...
38
votes
6
answers
7k
views
Companion to theoretical physics for working mathematicians
In the Princeton Companion to Mathematics one reads that even pure mathematicians should know some theoretical physics and applied mathematics. What are some well-organized comprehensive companions to ...
37
votes
4
answers
3k
views
Representation theory and elementary particles
I have been looking for a clear expository mathematical text on the relation between the theory of elementary particles and the representation theory of $U(1), SU(2), SU(3)$, I was very disappointed ...
- 1,619
34
votes
6
answers
4k
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 ...
- 1,212
33
votes
8
answers
3k
views
Motivation and physical interpretation of the Laplace transform
Concerning the one-sided Laplace transform,
$$\mathcal{L}\{f\}(s) = \int_0^\infty f(t)e^{-st} dt$$
what is a motivation to come up with that formula? I am particularly interested in "physical&...
- 545
31
votes
6
answers
8k
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 ...
- 25.9k
28
votes
5
answers
6k
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 ...
- 5,819
28
votes
3
answers
3k
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. ...
- 115k
27
votes
11
answers
4k
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 non-...
- 2,601
26
votes
2
answers
2k
views
Runner's High (Speed)
I find the following mind-boggling.
Suppose that runner $R_1$ runs distance $[0,d_1]$ with average speed $v_1$. Runner $R_2$ runs $[0,d_2]$ with $d_2>d_1$ and with average speed $v_2 > v_1$. I ...
- 45.5k
23
votes
5
answers
5k
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 ...
- 13.2k
23
votes
5
answers
7k
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 ...
- 21.1k
22
votes
6
answers
15k
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 ...
- 15.1k
21
votes
1
answer
1k
views
Fully extended TQFT and lattice models
I often read that fully extended TQFTs are supposed to classify topological phases of matter. So I would like to understand the formal nature of fully extended TQFTs on a more direct physical level (...
- 2,901
20
votes
6
answers
3k
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 ...
20
votes
5
answers
7k
views
Applications of set theory in physics
In the introduction of the paper "Links between physics and set theory", the following quote of Eris Chric is stated:
"Set theory perhaps is too important to be left just to ...
19
votes
4
answers
2k
views
Applications of complex exponential
In calculus we learn about many applications of real exponentials like $e^x$ for bacteria growth, radioactive decay, compound interest, etc. These are very simple and direct applications. My question ...
- 199
18
votes
9
answers
5k
views
How does a Masters student of math learn physics by self?
I am a Masters student of math interested in physics. When I was an undergraduate, I took the introductory course of physics, but it is just slightly harder than high school physics course. To be ...
- 183
17
votes
0
answers
245
views
Approximation of the effective resistance on Cayley graph
Let $\Gamma$ be a finitely generated group, and denote by $G$ the Cayley graph of $\Gamma$. Denote by $d_R$ the resistance distance metric on this graph. The resistance distance metric between the ...
- 395
16
votes
3
answers
695
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 ...
16
votes
1
answer
736
views
From a physicist: How do I show certain superelliptic curves are also hyperelliptic?
As the title suggests, I am a physicist and have a question about how to show certain superelliptic curves are also hyperelliptic. The superelliptic Riemann surfaces in question has the form $$w^n = \...
- 163
15
votes
6
answers
3k
views
Maxwell equations as Euler-Lagrange equation without electromagnetic potential
In (mathematical) physics many equations of motion can be interpreted as Euler-Lagrange (EL) equations. The Maxwell equation for electromagnetic (EM) field (say in vacuum and in absence of charges) ...
- 21.1k
15
votes
9
answers
4k
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, ...
- 1,212
15
votes
1
answer
713
views
Digital physics and "Gandy-like" machines
Various physicists, famously John Wheeler, have asserted that physical information is the central object of study in physics, in the sense that an object or concept is "physically meaningful" if it ...
- 3,522
14
votes
4
answers
5k
views
Which edition of Philosophiae Naturalis Principia Mathematica of Isaac Newton would you recommend to me?
I'm searching for a good edition of Philosophiae Naturalis Principia Mathematica of Isaac Newton in English. Which edition of the Principia can you suggest me? If it's possible, cheap and similar to ...
- 141
14
votes
1
answer
1k
views
Hilbert's sixth problem and QFT description
The Wikipedia entry on Hilbert's sixth problem about QFT description is “Since the 1960s, following the work of Arthur Wightman and Rudolf Haag, modern quantum field theory can also be considered ...
- 3,000
14
votes
2
answers
3k
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 ...
- 1,653
13
votes
1
answer
6k
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 ...
12
votes
4
answers
5k
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 ...
- 183
12
votes
2
answers
2k
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 ...
11
votes
4
answers
1k
views
Literature for gauge field theory on the lattice in geometrical formulation
I have found an article by Huebschmann, Rudolph and Schmidt about "A Gauge Model for Quantum Mechanics on a Stratified Space" and I am very interested in this subject, but I don't have any ...
11
votes
2
answers
2k
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.
CROSS-...
- 565
11
votes
3
answers
3k
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 ...
- 5,375
11
votes
3
answers
2k
views
On mathematical studies of the Mpemba effect
Since the days of Aristotle and Descartes, it has been known that under certain circumstances warm water freezes faster than cold water. This effect is now commonly known as the Mpemba effect, named ...
- 1,472
11
votes
1
answer
640
views
Importance of the principal bundle in Chern-Simons theory
This is a very basic beginners question about Chern-Simons theory. The configurations that we sum over to get the partition function are given by a Lie-algebra valued 1-form $A$ on a topological 3-...
- 2,901
11
votes
2
answers
572
views
What are the topological phases of quantum Hall systems?
(Fractional) quantum Hall systems are $2+1$-dimensional models which are said to possess topological order. One (maybe even complete) set of invariants of topological phases in $2+1$ dimensions is ...
- 2,901
11
votes
1
answer
2k
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 ...
- 8,508
11
votes
1
answer
1k
views
State of rigorous effective quantum field theories
It's well-known that there are no rigorously constructed and physically relevant QFTs. There is, however, a lot of mathematical work on effective field theories and renormalization, such as the books ...
- 269
11
votes
1
answer
463
views
D'Alembert's Principle: rigorous formulation using notions from modern differential geometry
Is there a rigorous definition of D'Alembert's principle of virtual dynamic work in the language of differential geometry? Some questions I'm hoping to answer are:
How to view the configuration space ...
- 111
10
votes
4
answers
2k
views
Why the unreasonable applicability of complex numbers in physics/engineering? [duplicate]
After years of using complex numbers in every kind of analysis of physical and electrical engineering problems I am starting to wonder: why is this particular algebra so effective in modelling the ...
- 217
10
votes
2
answers
1k
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 ...
- 151k
10
votes
1
answer
990
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. ...
- 167
10
votes
1
answer
1k
views
Mathematics of Chiral Rings
Let $A$ be a graded vector space, and suppose that two commuting differentials $d_1$ and $d_2$ of degree +1 act on $A$, such that $A$ equipped with either is a chain complex.
We now construct $C(A)$, ...
- 2,273