All Questions
Tagged with physics mp.mathematical-physics
94 questions
3
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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....
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6
votes
0
answers
371
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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 ...
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25
votes
5
answers
8k
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 ...
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153
votes
27
answers
50k
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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 ...
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1
vote
0
answers
204
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Are causally isomorphic spacetimes Wick-related?
Take the time-orientable spacetimes $(M_1,g_1)$ and $(M_2,g_2)$ that are locally(to be clarified below) Wick-related and both are globally Wick-rotatable(to be clarified below) to the same Riemannian ...
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4
votes
1
answer
670
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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_{...
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1
vote
0
answers
228
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Is the topological dimension of spacetime fixed for causally isomorphic spacetimes?
Suppose time-oriented spacetimes $(M_1 , g_1)$ and $(M_2, g_2)$ are not homeomorphic under their manifold topologies $\mathcal{M}_1$ and $\mathcal{M}_2$ respectively.
The Lorentzian metrics $g_1$ and $...
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1
vote
0
answers
170
views
Order isomorphism + manifold homeomorphism => path topology homeomorphism?
Suppose time-oriented spacetimes $(M_1 , g_1)$ and $(M_2, g_2)$ are homeomorphic under their manifold topologies $\mathcal{M}_1$ and $\mathcal{M}_2$ respectively.
Let's call this map $\phi: (M_1, \...
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1
vote
1
answer
361
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Can the Causal Structure recover the manifold topology for non-chronological spacetimes?
Given a time-oriented spacetime $(M,g)$, a binary relation $\ll$ can be defined on this spacetime where $p \ll q$ for $p, q \in M$ if and only if there exists a time-like path connecting $p$ and $q$.
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3
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1
answer
244
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inclusion of von Neumann algebras implies reversing inequality of its modular operators
I'm working with von Neumann algebras and I stumbled with this statement in a work of Borchers (1999)
Since $\mathcal N \subseteq \mathcal M$, it follows by standard arguments that $\Delta_{\mathcal ...
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0
votes
0
answers
100
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I'm looking for the NLab page on particle species
This is just a reference request.
I came across an NLab page on particle species described as certain vector bundles. But I can't seem to find it again when I searched recently.
If someone can point ...
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14
votes
1
answer
1k
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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 ...
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27
votes
11
answers
4k
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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-...
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54
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6
answers
13k
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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 ...
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1
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1
answer
294
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Temporal evolution of a globally hyperbolic spacetime
Any globally hyperbolic spacetime can be assigned a global function of time as Hawking has demonstrated for stably causal spacetime. (Any globally hyperbolic spacetime is also stably causal).
For ...
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1
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0
answers
80
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Biot-Savart-like integral for a toroidal helix
The following problem originates from Physics, so I apologize if I will not use a rigorous mathematical jargon.
Let us consider a toroidal helix parametrized as follows:
$$
x=(R+r\cos(n\phi))\cos(\phi)...
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3
votes
1
answer
249
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Interesting question about the Thomson problem for arbitrary number of electrons
This question is crossposted from here I believe this is a pretty hard question and so I decided to repost the question in the Math Overflow forum. If there is something wrong with doing this, I am ...
- 128k
3
votes
1
answer
146
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Applications of maximal surfaces in Lorentz spaces
I have been working on minimal surfaces, only recently learnt about maximal surfaces and "maxfaces" in Lorentz spaces.
I can clearly see the mathematical motivations. But I wonder if zero-...
- 21.5k
0
votes
1
answer
282
views
Mathematical characterization of gravitational geons as reference request, and their properties as main question
I've edited (ten days ago) a question on Physics Stack Exchange, this Mathematical characterization of gravitational geons, post with identifier 726281 the users of the site were kind adding in the ...
- 188k
10
votes
1
answer
566
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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 ...
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-1
votes
1
answer
437
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Harmonic function in infinite domain in $\mathbb{R}^3$, constant on the boundary and decaying as $1/r^2$
EDIT: Let $\Omega\subset \mathbb{R}^3$ be a bounded domain with smooth connected boundary. Let $f\colon \mathbb{R}^3\backslash \Omega \to \mathbb{R}$ be a continuous function which is harmonic in $\...
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2
votes
1
answer
371
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Examples of ODEs with complex constant coefficients and applications to physics?
This question is asked on stackexchange: Are there examples for ODEs with complex coefficients with applications in physics?
but received no answers. I am reposting it here on the hope that it catches ...
- 6,045
11
votes
4
answers
2k
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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 ...
- 1,446
4
votes
0
answers
116
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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 ...
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15
votes
6
answers
4k
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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) ...
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16
votes
1
answer
753
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 $$w^n = \...
- 148k
2
votes
0
answers
171
views
Is there an example Hamiltonian that is uncomputable?
In a paper from 2015 Toby S. Cubitt et al showed that the problem of determining the existence of a band gap in the excitation spectrum of a quantum many-body system, was undecidable. This result ...
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2
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4
answers
336
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EM-wave equation in matter from Lagrangian
Note
I am not sure if this post is of relevance for this platform, but I already asked the question in Physics Stack Exchange and in Mathematics Stack Exchange without success.
Setup
Let's suppose a ...
2
votes
1
answer
164
views
Vacuum state generating functional
In Theorem 1 of this paper Segal stablish a relation between states and generating functionals.
He assert that in order to $\mu$ be a generating functional must satisfy
$$
\sum_{j,k\in F} \mu (z_j-...
11
votes
1
answer
1k
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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 ...
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4
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2
answers
2k
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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
923
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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 ...
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3
votes
4
answers
1k
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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 ...
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3
votes
1
answer
386
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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 ...
- 118k
1
vote
1
answer
116
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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 ...
- 188k
9
votes
1
answer
800
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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)...
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3
votes
2
answers
434
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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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11
votes
2
answers
640
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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 ...
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70
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10
answers
11k
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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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2
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1
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89
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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 ...
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5
votes
0
answers
240
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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 ...
- 3,830
11
votes
1
answer
682
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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-...
- 5,760
21
votes
1
answer
1k
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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 (...
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4
votes
0
answers
164
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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....
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34
votes
6
answers
5k
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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 ...
2
votes
0
answers
131
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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; ...
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3
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0
answers
159
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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
130
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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 ...
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2
votes
1
answer
712
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Generating Functional for the Dirac Field, equivalence of expressions
As with the Klein-Gordon field, we can alternatively derive the Feynman rules with the free Dirac theory by means of a generating functional. In analogy with the scalar field theory where $Z[J]$ is ...
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43
votes
7
answers
13k
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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 ...
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