Questions tagged [physics]
For questions about mathematical problems arising from physics, the natural science studying general properties of matter, radiation and energy.
194 questions
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
10
votes
1
answer
566
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 ...
- 101
10
votes
1
answer
1k
views
Self-tightening knot
Is there a way, for some finite $L>1$, to tie two length $L$ 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 ...
- 163
9
votes
5
answers
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 ...
9
votes
1
answer
800
views
Why the least action principle is always (?) used in this particular form?
The least action principle in (mathematical) physics says the following. Given a system, e.g. collection of particles, whose motion satisfies a known system of differential equations (of second order)...
- 21.8k
9
votes
2
answers
848
views
$\zeta$-function regularized determinants
In (mathematical) physics in order to compute path integrals one often makes an infinite dimensional change of variables and uses infinite Jacobian as a purely formal expression. This step is done in ...
- 21.8k
9
votes
2
answers
1k
views
What is the BRST-anti-BRST formalism?
What is the BRST-anti-BRST formalism?
Is the Sp(2) doublet the ghost, antighost pair?
Introductory accounts of this subject seem to be hard to find. I would appreciate a reference for someone who ...
- 3,880
9
votes
1
answer
385
views
Why are discreteness and smoothness in physics inversed with respect to geometry?
In a closed (say differentiable) Riemannian manifold you see only continuous features when looking at small neighbourhoods of points. From afar,
discrete features appear ((co)homology, closed ...
- 17.9k
9
votes
0
answers
371
views
Which of the physics dualities are closest in essence to the Spanier-Whitehead duality (with a subquestion)?
First of all, what I want to ask is slightly more elaborate than what stands in the title (hence the subquestion).
I am telling this since as it is, the title contains a meaningful question, but it ...
- 18.4k
8
votes
1
answer
432
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 ...
- 9,720
8
votes
0
answers
1k
views
Is there any physics theory which is similar to these analogies?
Since I am doing this little "research" project on my spare time and in my physical neighborhood there are not many people to discuss these ideas, I wanted to share with you a small point of ...
- 3,064
7
votes
4
answers
3k
views
Exercises in Lie group theory for physics
I teach a course on (Lie) group theory for physics at the level of senior undergraduates.
I follow basically the book by Georgi "Lie algebras in particle physics". So I teach them the groups SU(2), ...
user16974
7
votes
1
answer
2k
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 ...
- 17.5k
7
votes
1
answer
514
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 hemisphere. ...
- 1,663
7
votes
0
answers
125
views
Charge distribution of closed surfaces
Consider a closed surface $\Sigma$ which bounds a solid $\Omega$ in ${\mathbb R}^3$. Assume some electric charges, say totally $Q$, is distributed on $\Sigma$ and reaches an "equilibrium" state. In ...
- 79
6
votes
4
answers
709
views
Higgs mechanism from a deformation quantization point of view
Is it possible to describe the Higgs mechanism from a deformation quantization point of view? How would one do it? Are there aspects of the Higgs mechanism and Higgs particle which one may see clearer ...
- 1,222
6
votes
2
answers
974
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 ...
- 65
6
votes
1
answer
423
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 ...
- 61
6
votes
1
answer
403
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 $U\in SU(n)$.
...
- 1,612
6
votes
0
answers
371
views
What is the predictive power of each object in QFT, and how are they related? [closed]
My background is not in physics or mathematical physics, so this question is mostly out of ignorance, and probably easily known to experts.
Basic Setup
You begin with a spacetime $M$. (Minkowski in ...
- 557
5
votes
2
answers
4k
views
Two point function of a free scalar field in Euclidean space-time
This question was previously asked here
https://physics.stackexchange.com/questions/251927/two-point-function-of-a-free-massless-scalar-field-in-euclidean-space-time
though I did not get there an ...
- 21.8k
5
votes
2
answers
1k
views
origin of analogy "primes as the atoms of number theory/ arithmetic"
a math student recently challenged me on the old comparison/ analogy of prime numbers to "the atoms of number theory or arithmetic" and then was wondering the origin of the phrase.
where does this ...
- 529
5
votes
2
answers
892
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 ...
- 7,831
5
votes
1
answer
354
views
Gadgets as primality tests
From the literature, showed below, I know two gadgets that provide a way to know if a positive integer (a positive quantity of units) is composite or a prime number. I would like to know if in the ...
5
votes
1
answer
3k
views
Why Chern numbers (integral of Chern class) are integers?
I am a physics student trying to self-learn Chern numbers and Chern class. The book I am learning (Nakahara) introduces the total Chern class as an invariant polynomial of local curvature form $F$
$P(...
- 81
5
votes
2
answers
1k
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
$$\cos\left(t\right)\partial_{x}\mathbf{u}+\sin\left(t\right)\partial_{y}\mathbf{u}+...
- 245
5
votes
2
answers
953
views
Singular K3 -- mathematical meaning?
There's a very interesting text by Cumrun Vafa called Geometric Physics.
Here I'm particularly interested in Chapter 4, where we take a Calabi-Yau manifold presented as a degenerating fibration:
...
- 15.1k
5
votes
1
answer
321
views
Quantum tunneling on the line with non-symmetric double well potential
Consider the Schroedinger equation on the line
$$i\frac{\partial \Psi(x,t)}{\partial t}=[-\frac{d^2}{dx^2}+V(x)]\Psi(x,t),$$
where one assumes that $V(x)\to +\infty$ as $|x|\to +\infty$, and $V$ has ...
- 21.8k
5
votes
1
answer
214
views
Interpretation for a condition in fluid dynamics
I have been working with some mathematical models in biology and fluid mechanics. My problem is about
the interpretation of a condition that I found for a vector
representing the velocity of a fluid. ...
- 171
5
votes
0
answers
126
views
Particles sent into the same direction with uniformly distributed speed
Fix a positive integer $n$. Every second, a particle is sent along a straight line from a fixed position in a fixed direction, at a random integer speed chosen uniformly in $\{1,\ldots, n\}$ meters ...
- 48.9k
5
votes
0
answers
240
views
Does Dijkgraaf-Witten theory have a time-reversal symmetry?
By having a time-reversal symmetry I mean that there is a local anti-unitary symmetry (representing the non-trivial element of $Z_2$) of the state-sum construction (or, if you want, of the associated ...
- 3,001
5
votes
0
answers
274
views
$S$-matrix in QED in 2d space-time
I am not completely sure that this question is appropriate for this site, but I have asked a similar question here https://physics.stackexchange.com/questions/271372/s-matrix-in-qed-in-2d-space-time ...
- 21.8k
4
votes
2
answers
2k
views
Reference for mathematical Palatini formalism of general relativity
I know that this is maybe not a research level question, but since the topic is quite special, I thought that the chance to get some reference is higher in this community.
I am looking for a reference ...
- 1,171
4
votes
1
answer
551
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
1
answer
403
views
How are spatial coordinate systems in physics defined?
Grothendieck once asked "What is a meter?" (https://golem.ph.utexas.edu/category/2006/08/letter_from_grothendieck.html). This innocent sounding question, made me to think about how ...
- 3,064
4
votes
2
answers
1k
views
Gauge-theoretic formulation of Maxwell equations [duplicate]
Does any one know how to write the Maxwell equations as an equation on a principal $U(1)$-bundle?
In Freed & Uhlenbeck's Instantons and Four manifolds, the authors claim that the Maxwell ...
- 957
4
votes
1
answer
705
views
Why are solenoidal fields called solenoidal?
A solenoidal tangent field, mathematically speaking, is one whose divergence vanishes. They are also called incompressible. I understand why they are called incompressible — a fluid flow is called ...
- 2,369
4
votes
1
answer
670
views
Formula involving Wigner's 3j symbols and integration over irreducible representations of SU(2)
$\DeclareMathOperator\SU{SU}$In some calculations, I saw the following formula
$$\int_{\SU(2)}\,\mathrm{d}g\,D^{j_{1}}_{m_{1}n_{1}}(g)D^{j_{2}}_{m_{2}n_{2}}(g)D^{j_{3}}_{m_{3}n_{3}}(g)=(-1)^{j_{1}+j_{...
- 1,171
4
votes
2
answers
477
views
Experiments physically performable in a finite amount of time whose results are independent of ZFC [closed]
In On independence and large cardinal strength of physical statements we see that their are physical statements which are independent of ZFC, and even strong cardinal axioms. There were many answers, ...
- 6,353
4
votes
1
answer
232
views
Sites for seeking possible collaborations [closed]
As a material scientist, I have recently constructed algorithms for solving ground state of arbitrary cluster interactions models and prepared publications in the field of physics and material science....
- 867
4
votes
1
answer
923
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 ...
- 1,893
4
votes
3
answers
4k
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
...
- 141
4
votes
1
answer
103
views
Deriving integral in Gaiotto-Tommasiello theory
I was looking at a paper by Takao Suyama on GT theory, and I couldn't figure out how he derived his formula (3.59):
$$\frac{1}{\pi}\int_a^bdx\frac{1}{z-x}\frac{\sqrt{(z-a)(z-b)}}{\sqrt{|(x-a)(x-b)|}}\...
- 161
4
votes
1
answer
185
views
reference for higher spin - not gravitational nor stringy
Other than the papers of Berends, Burgers and van Dam, are there any papers that study the general case of deforming a free field theory with higher spin fields to be interactive?
- 3,880
4
votes
1
answer
738
views
Helmholtz equation Poynting vector integral
The Maxwell's equation for harmonic time dependent field in vacuum is
\begin{align}
\nabla \times B + i\omega E &= 0\\
\nabla \times E - i\omega B &= 0 \\
\nabla \cdot B &= 0 \\
\nabla \...
- 2,239
4
votes
1
answer
645
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 ...
- 31
4
votes
0
answers
116
views
Superspace derivation of supersymmetric non-linear sigma model in Supersolutions by Deligne and Freed
I am having a little trouble understanding passage from the linear to the non-linear sigma model in Section 4.1 of Supersolutions by Deligne and Freed. Most of my confusion comes down to the ...
user482049
4
votes
0
answers
164
views
List of Replica Symmetry results for different models?
Does anyone know of a good source that might have a list of problems or models along with what kind of replica symmetry they are conjectured to have?
I am aware of some of the more famous results, e....
- 435
4
votes
0
answers
219
views
Why do we care about simplicity of the spectrum in Oseledets' theorem?
Oseledets' theorem is a fundamental result in Ergodic theory (see for example here, or Chapter 4 of Lectures on Lyapunov Exponents by Marcelo Viana).
The simplicity of the spectrum has been studied ...
- 1,805
4
votes
0
answers
334
views
Unusual generalization of the law of large numbers
I have seen in physical literature
an example of application of a very unusual form of the law of large numbers. I would like to understand how legitimate is the use of it, whether there are ...
- 21.8k