# Questions tagged [physics]

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

147
questions

**3**

votes

**2**answers

189 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 already asked this ...

**1**

vote

**0**answers

23 views

### Angular velocity from rotation matrix difference [closed]

I am working on something for a game. I need to calculate the angular velocity, however in my situation I only have access to the previous rotation matrix and the current rotation matrix. My angular ...

**1**

vote

**0**answers

56 views

### Is there an analytic formula (or even a name…) for a plane curve with curvature inversely proportional to x?

I'm interested in plane curves with curvature inversely proportional to distance from the axis:
$$\kappa(t) = \left(\frac{x'(t) y''(t) - y'(t)x''(t)}{(x'(t)^2 + y'(t)^2)^{3/2}} \right) = \frac{1}{a x(...

**1**

vote

**1**answer

149 views

### What is the precise relationship between real Poisson algebras and commutative $C^*$ algebras?

I've been teaching myself quantum mechanics, and I realized that I'm missing something fundamental. Namely, there are two pictures that I don't know how to reconcile:
Quantum Mechanics generalizes ...

**3**

votes

**4**answers

434 views

### Applications of Hamiltonian formalism to classical mechanics

In many courses in theoretical classical mechanics Hamiltonian formalism takes an important place. However I did not see it applied to problems of classical mechanics (unless one expands the scope of ...

**11**

votes

**5**answers

2k 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) ...

**1**

vote

**1**answer

86 views

### Is there a Bell inequality for each of $2\times 2$, $3\times 1$, $2\times1\times1$ and $1\times1\times1\times1$ configurations?

There was no answer in https://physics.stackexchange.com/questions/600494/is-there-a-bell-inequality-for-2-times-2-and-1-times1-times1-times1-configur. Hence posting in mathoverflow on the possibility ...

**9**

votes

**1**answer

647 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)...

**2**

votes

**2**answers

149 views

### Classification of Lagrangians with given Euler-Lagrange equations

In (mathematical) physics the equations of motion of a system of particles are often interpreted as Euler-Lagrange equations for appropriate Lagrangian $L=L(x,\dot x,t)$ where $x$ is a collection of ...

**2**

votes

**0**answers

91 views

### What is the relationship between Riemannian and sympletic musical isomorphisms on the cotangent bundle?

Let $M$ be a smooth manifold. Its cotangent bundle naturally has a symplectic structure, and this gives rise to musical isomorphisms. These musical isomorphisms are the ones from physics that relate ...

**4**

votes

**1**answer

89 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)|}}\...

**3**

votes

**1**answer

146 views

### Monotile that tiles when you apply a rubber band

My (non-mathematician) friend asked me a physics/tilings question that maybe someone here is interested in dissecting, or can point to the literature if this problem has been studied.
Does there ...

**1**

vote

**1**answer

49 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

138 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

316 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 ...

**5**

votes

**1**answer

314 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

77 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 ...

**66**

votes

**10**answers

10k 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

102 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.

**10**

votes

**2**answers

276 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

18 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

175 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

435 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-...

**17**

votes

**1**answer

837 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

60 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

97 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

116 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

121 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

100 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

83 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

339 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

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 ...

**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

105 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

295 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 ...

**5**

votes

**1**answer

155 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

3k 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 ...

**36**

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

92 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

92 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

80 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 ...

**4**

votes

**2**answers

437 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

1k 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

80 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

333 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

102 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

292 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 ...

**32**

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

86 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 ...