# Questions tagged [physics]

For questions about mathematical problems arising from physics, the natural science studying general properties of matter, radiation and energy.

137
questions

**-3**

votes

**0**answers

27 views

### RPM Calculation [closed]

How can I determine the RPM needed to make an object travel 120in on a conveyor belt in 1min?
I know 3 things:
1.) the length of the conveyor belt (distance between first and last wheel) is 120in
2....

**1**

vote

**0**answers

30 views

### Set of eigenvalues of the boundary problem

I'm looking for the results about the set of eigenvalues of boundary problem for differential equation
\begin{equation}
\bigl(p(x) u'(x; \lambda) \bigr)' + q(x) u(x; \lambda) = -\lambda w(x) u(x; \...

**2**

votes

**0**answers

132 views

### geometrical or physical interpretation of second Chern classes of Calabi-Yau threefold

It's my first post.
Consider Calabi-Yau threefold $M$ and its tangent bundle $TM$. I know $c_1(TM)=0$ means metric on $M$ is a solution of vacuum Einstein equation. Then my question is "are there any ...

**2**

votes

**1**answer

301 views

### Applications of Generalized Geometry to Theoretical Physics [closed]

I'm looking for some topics on Generalized Geometry applied to Physics for a master thesis. I took an introductory course last year, and I have a degree in both Mathematics and Physics. I would ...

**4**

votes

**1**answer

278 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 ...

**2**

votes

**1**answer

73 views

### Sufficient conditions for unitarity of a representation of a Lie Superalgebra

Suppose we have a Lie superalgebra with triangular decomposition:
\begin{equation}
\mathfrak{g} = \mathfrak{g}^{+} \oplus \mathfrak{g}^{0} \oplus \mathfrak{g}^{-}
\end{equation}
I've seen it stated ...

**64**

votes

**10**answers

9k 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 ...

**0**

votes

**0**answers

98 views

### Cardinal Invariants and Physics

There are many applications of topology to physics, but I wonder if there is a known application of cardinal invariants to physics.

**0**

votes

**0**answers

118 views

### Are all cellular automata models related to the Bekenstein bound and the holographic principle?

Cellular automata are discrete models which have a regular finite dimensional grid of cells, each in one of a finite number of states, such as on and off.
There are various scientists that have ...

**10**

votes

**2**answers

207 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**

votes

**0**answers

17 views

### Difference Between Total Least Squares Plane and Plane Orthogonal to Principal Axis of Inertia Tensor

Given a finite set $P$ of points in $\mathbb{E}^3$ , one can calculate an approximating plane either as the solution of a Total Least Squares problem or by interpreting the problem physically, ...

**4**

votes

**0**answers

163 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 ...

**11**

votes

**1**answer

351 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-...

**16**

votes

**1**answer

698 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 (...

**0**

votes

**0**answers

58 views

### Energy-minimizing set of discrete points in a bounded domain

Let $\Omega \subset \mathbb{R}^3$ be a smooth, bounded domain.
Let $x_1,\ldots,x_n \in \overline{\Omega}$ be chosen so as to minimize
$$
\sum_{1\leq i<j\leq n} \frac{1}{|y_i - y_j|}
$$
over all ...

**4**

votes

**0**answers

86 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....

**2**

votes

**0**answers

115 views

### Questions about using mathematical methods to prove the Caratheodory's Concept of Temperature

Caratheodory's Concept of Temperature is not Carathéodory's theorem.
I have tried,but I found nothing about this question by searching online.
This is what I have seen in a thermodynamics textbook; ...

**3**

votes

**0**answers

110 views

### Does there exist a compactly supported integrable function with infinite Coulomb energy?

The title of the question pretty much says it all. I am looking for a function $f\in L^1(\Omega)$, where $\Omega \subset \mathbb{R}^3$ is a bounded domain, such that
$$
E[f] = \iint\limits_{\Omega\...

**1**

vote

**1**answer

91 views

### Localization of solutions for time-dependent Schroedinger equation

I've been playing around with numerical solutions to the Schroedinger equation and I came across something that feels very natural, but I was not able to prove it with the math I know.
The ...

**2**

votes

**0**answers

80 views

### 1D Schrödinger Equation with Measure-Valued Coefficients

I've been looking at one of the simplest systems I can think of: a one-dimensional infinite square well on $[0,1]$ with Hamiltonian given by the following:
$$\hat{H}=-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}...

**3**

votes

**2**answers

298 views

### Legendre equation: An interpretation [closed]

I am a student of physics and, especially in quantum mechanics, we are presented with the Legendre equation:
\begin{eqnarray}
(1-x^2)y''-2xy'+l(l+1)y=0.
\end{eqnarray}
Doing some calculations, we ...

**26**

votes

**2**answers

1k 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 ...

**3**

votes

**1**answer

361 views

### Does current follow the path(s) of least (total) resistance?

Consider Poisson equation $\nabla \cdot (\sigma(x)\nabla u)=0$ in a domain $D$, where $\sigma(x)$ is the spatially dependent conductivity. On the boundary we have $2$ electrodes $E_1$ and $E_2$ (...

**3**

votes

**0**answers

98 views

### Partial Liouville equation

In my master's thesis, I worked on mathematical multi-scale models for muscle tissue. Now after finishing it, I would like to find out if one direction could be a research topic for my PhD.
At one ...

**2**

votes

**1**answer

237 views

### PDE’s whose solutions can be presented using path integrals

It is well known that solutions of the Schroedinger equation and of the heat equation can be presented using path integrals:
$$\psi(x,t)=\int K(x,t;y,0)\psi(y,0)dy,$$
where the kernel $K(x,t;y,0)$ is ...

**4**

votes

**1**answer

129 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 ...

**14**

votes

**4**answers

2k 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 ...

**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 ...

**34**

votes

**4**answers

5k 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) ...

**2**

votes

**0**answers

86 views

### Is this correct: Inflection points of Euler number graph in Island-Mainland transition correspond to spanning cluster site percolation threshold?

I'm writing with respect to the paper Khatun, Dutta, and Tarafdar - "Islands in Sea" and "Lakes in Mainland" phases and related transitions simulated on a square lattice.
Here's a link to a PDF ...

**1**

vote

**1**answer

88 views

### wave speed and travelling wave

I have seen a lot of work has been done in the context of travelling wave. For example the work of McKenna and Chen in Journal of Differential Equations Volume 136, Issue 2, 20 May 1997, Pages 325-355....

**0**

votes

**0**answers

75 views

### Movement of a random walk in the limit (a particle in diffusion)

I asked this question in Math Exchange and obtained no answer.
Let $X(t)$ be a stochastic process in time such that $X(0)=0$ and, at each increment of time $\Delta t$, it can move $h$ units in space ...

**3**

votes

**2**answers

421 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, ...

**0**

votes

**0**answers

942 views

### What is a self-consistent equation in percolation theory

I was reading papers about percolation theory in which I was confused by the expression "self-consistent equation", for example in Temporal percolation in activity-driven networks. I read some ...

**1**

vote

**0**answers

78 views

### Diffraction across an absorbing wall

I need help finding the procedure for the solution of the following differential equation.
This is equation is: Find $u:\mathbb{R}^2 \to \mathbb{C}$ such that for $C>0$
$ \begin{cases} u_{xx}+ ...

**9**

votes

**0**answers

321 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 ...

**6**

votes

**0**answers

100 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 ...

**3**

votes

**1**answer

251 views

### Wave front set of vector-valued Dirac delta distribution

Context: I am reading a physics paper Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime which applies the notion of the wave front set to operator-valued ...

**30**

votes

**4**answers

2k 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 ...

**3**

votes

**0**answers

83 views

### Multiplicativity of $\zeta$-function regularized determinant

Let $A$ be a selfadjoint elliptic differential operator on a compact manifold. In mathematical physics and differential topology one often defines its determinant using the $\zeta$-function ...

**9**

votes

**2**answers

577 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 ...

**3**

votes

**1**answer

1k 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(...

**3**

votes

**0**answers

93 views

### Is there any connection between Lagrange points and the icosahedron?

Given the Newtonian two-body problem, one can ask if there are any orbits that allow a test particle to maintain a fixed configuration relative to the two bodies. In other words, in a frame that ...

**5**

votes

**0**answers

168 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 ...

**3**

votes

**1**answer

694 views

### Boundary conditions for Klein-Gordon equation

Let us consider the Klein-Gordon equation
$$(\Box +m^2)u=0,$$
where $u$ is a scalar valued function, $m\geq 0$, $\Box=\frac{\partial^2}{\partial x_0^2}-\sum_{i=1}^d\frac{\partial^2}{\partial x_i^2}$.
...

**13**

votes

**1**answer

494 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 ...

**4**

votes

**0**answers

186 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 ...

**4**

votes

**2**answers

2k 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 ...

**3**

votes

**1**answer

749 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 ...

**3**

votes

**1**answer

180 views

### Conserved quantities for the Cauchy momentum equation

I apologize if this question is too elementary for mathoverflow; I asked it (unsuccessfully) on MATH.SE first.
As a bit of background: one way to study the mechanics of deformation of a continuous ...