Questions tagged [physics]
For questions about mathematical problems arising from physics, the natural science studying general properties of matter, radiation and energy.
189
questions
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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 ...
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votes
0
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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 ...
- 473
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votes
1
answer
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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
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votes
1
answer
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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 ...
- 6,337
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1
answer
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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; \...
- 19
2
votes
0
answers
161
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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 ...
- 21
2
votes
1
answer
339
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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 ...
- 21
5
votes
1
answer
349
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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
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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 ...
- 61
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votes
10
answers
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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 ...
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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.
11
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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
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votes
0
answers
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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, ...
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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 ...
- 2,901
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votes
1
answer
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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-...
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1
answer
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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
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0
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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|}
$$
over all ...
- 401
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votes
0
answers
148
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List of Replica Symmetry results for different models?
Does anyone know of a good source that might have a list of problems or models along with what kind of replica symmetry they are conjectured to have?
I am aware of some of the more famous results, e....
- 425
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0
answers
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Questions about using mathematical methods to prove the Caratheodory's Concept of Temperature
Caratheodory's Concept of Temperature is not Carathéodory's theorem.
I have tried,but I found nothing about this question by searching online.
This is what I have seen in a thermodynamics textbook; ...
- 21
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votes
0
answers
148
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Does there exist a compactly supported integrable function with infinite Coulomb energy?
The title of the question pretty much says it all. I am looking for a function $f\in L^1(\Omega)$, where $\Omega \subset \mathbb{R}^3$ is a bounded domain, such that
$$
E[f] = \iint\limits_{\Omega\...
- 401
1
vote
1
answer
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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 ...
- 445
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0
answers
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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:
$$\hat{H}=-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}...
- 21
3
votes
2
answers
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Legendre equation: An interpretation [closed]
I am a student of physics and, especially in quantum mechanics, we are presented with the Legendre equation:
\begin{eqnarray}
(1-x^2)y''-2xy'+l(l+1)y=0.
\end{eqnarray}
Doing some calculations, we ...
26
votes
2
answers
2k
views
Runner's High (Speed)
I find the following mind-boggling.
Suppose that runner $R_1$ runs distance $[0,d_1]$ with average speed $v_1$. Runner $R_2$ runs $[0,d_2]$ with $d_2>d_1$ and with average speed $v_2 > v_1$. I ...
- 45.5k
3
votes
1
answer
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Does current follow the path(s) of least (total) resistance?
Consider Poisson equation $\nabla \cdot (\sigma(x)\nabla u)=0$ in a domain $D$, where $\sigma(x)$ is the spatially dependent conductivity. On the boundary we have $2$ electrodes $E_1$ and $E_2$ (...
- 532
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votes
0
answers
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Partial Liouville equation
In my master's thesis, I worked on mathematical multi-scale models for muscle tissue. Now after finishing it, I would like to find out if one direction could be a research topic for my PhD.
At one ...
2
votes
1
answer
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PDE’s whose solutions can be presented using path integrals
It is well known that solutions of the Schroedinger equation and of the heat equation can be presented using path integrals:
$$\psi(x,t)=\int K(x,t;y,0)\psi(y,0)dy,$$
where the kernel $K(x,t;y,0)$ is ...
- 21.1k
5
votes
1
answer
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Quantum tunneling on the line with non-symmetric double well potential
Consider the Schroedinger equation on the line
$$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 ...
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14
votes
4
answers
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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
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4
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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
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4
answers
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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
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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 ...
user119567
3
votes
1
answer
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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....
- 402
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votes
0
answers
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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 ...
- 141
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votes
2
answers
473
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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, ...
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0
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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 ...
- 211
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vote
0
answers
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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
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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 ...
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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
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1
answer
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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 ...
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37
votes
4
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3k
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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 ...
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0
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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 ...
- 21.1k
9
votes
2
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774
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$\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 ...
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5
votes
1
answer
3k
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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
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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 ...
- 1,404
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0
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$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 ...
- 21.1k
3
votes
1
answer
2k
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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, $m\geq 0$, $\Box=\frac{\partial^2}{\partial x_0^2}-\sum_{i=1}^d\frac{\partial^2}{\partial x_i^2}$.
...
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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
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0
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216
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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 ...
- 1,785
4
votes
2
answers
4k
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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 ...
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