All Questions
Tagged with physics mp.mathematical-physics
94 questions
3
votes
2
answers
447
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 ...
- 7,746
2
votes
0
answers
192
views
Diffusion equation on mixing of diffusing particles
I am trying to study mixing of diffusing particles like it was done by E. Ben-Naim On the Mixing of Diffusing Particles.
The picture below shows the idea how permutations and inversion numbers reflect ...
3
votes
1
answer
383
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 $E_2$ (...
- 188k
2
votes
1
answer
528
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 ...
- 1,105
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 ...
- 188k
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 ...
- 191
2
votes
0
answers
103
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 ...
- 12.9k
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
0
votes
0
answers
3k
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 ...
- 26.3k
3
votes
2
answers
389
views
Translation of an article
I need to read this article
"On the spectrum of an energy operator for atoms with fixed nuclei in subspaces corresponding to irriducible representations of permutation groups"
authors:G.Zhislin, A. ...
CommunityBot
- 1
3
votes
1
answer
512
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 ...
37
votes
4
answers
4k
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 ...
CommunityBot
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3
votes
0
answers
94
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 ...
CommunityBot
- 1
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 ...
CommunityBot
- 1
20
votes
5
answers
8k
views
Applications of set theory in physics
In the introduction of the paper "Links between physics and set theory", the following quote of Eris Chric is stated:
"Set theory perhaps is too important to be left just to ...
CommunityBot
- 1
3
votes
1
answer
2k
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, $m\geq 0$, $\Box=\frac{\partial^2}{\partial x_0^2}-\sum_{i=1}^d\frac{\partial^2}{\partial x_i^2}$.
...
CommunityBot
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15
votes
1
answer
748
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 ...
- 188k
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 ...
CommunityBot
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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
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?
- 188k
38
votes
6
answers
7k
views
Companion to theoretical physics for working mathematicians
In the Princeton Companion to Mathematics one reads that even pure mathematicians should know some theoretical physics and applied mathematics. What are some well-organized comprehensive companions to ...
CommunityBot
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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 ...
- 188k
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
-2
votes
1
answer
147
views
What are the formula of representation of quasicrystals and the law or mechanism of the formation [closed]
I vaguely recall that formula of representation of quasicrystals is relevant to tiling plane,and tiling plane without period is relevant to recursiveness, and do not know the mechanism or physics ...
- 54.2k
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 ...
- 29.2k
15
votes
9
answers
4k
views
Newton equations, second order equation and (im)possible motions
I am am currently studying Newtonian mechanics from a conceptional and axiomatic point of view. Now, if I am not mistaken, one (but surely not all) statement of Newtons second law about nature is, ...
CommunityBot
- 1
29
votes
3
answers
4k
views
How can simple physical "proofs" of mathematical facts be made rigorous?
Mark Levi's The Mathematical Mechanic is a book of examples of how physical reasoning can be used to solve mathematical problems; another couple of examples is in this blog post at Concrete Nonsense. ...
CommunityBot
- 1
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 ...
CommunityBot
- 1
106
votes
3
answers
10k
views
Has the Lie group E8 really been detected experimentally?
A few months ago there were several math talks about how the Lie group E8 had been detected in some physics experiment. I recently looked up the original paper where this was announced,
"Quantum ...
2
votes
0
answers
115
views
The condition of maximality in branching rules of $SO$ group representations
Let the highest weight of a $SO(2n+1)$ representation be given as $(m_1,m_2,...,m_n)$ ($m_1\geq m_2 \geq .. \geq m_n \geq 0$) and the highest weight of a $SO(2n)$ representation be $(s_1,s_2,...,s_n)$ ...
- 1,893
3
votes
0
answers
654
views
In the topos-theoretic interpretation of Physics by Isham & Doering what role does intuitionistic logic play? [closed]
I've asked this question on Physics.SE but was advised to ask it here.
Isham & Doering have written a series of papers exploring how to ground physics in topoi. Now the internal logic of topoi is ...
CommunityBot
- 1
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. ...
- 2,097
31
votes
6
answers
8k
views
Explanations for mathematicians, about the falsifiability (or not) of string theory [closed]
Like many other mathematicians, I think string theory very attractive. This theory has wonderfully influenced many new topics in mathematics (I myself have worked on one of them), but it's not the ...
CommunityBot
- 1
2
votes
1
answer
2k
views
What is the "fundamental theorem of invariant theory" ?
The basic question I guess can be formulated as - given two integers $N_f$ and $N_c$ what are the ways in which the fundamental and the anti-fundamental representations of $U(N_f)$ be combined to get ...
CommunityBot
- 1
3
votes
1
answer
212
views
Three body problem with point interactions
I've studied the HVZ theorem for the three body problem interacting with regular potentials. I'd like to extend this result to the three body problem with point interactions (delta potentials).
Is ...
- 188k
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 ...
- 1,038
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 ...
- 3,081
15
votes
2
answers
3k
views
What do correlation functions compute in CFT?
I would like to understand what correlation functions compute in Conformal Field Theory in mathematics. Let me begin with basic definitions. We define a free boson field $\phi(z)$ as a formal power ...
- 5,546
0
votes
1
answer
126
views
orthotropic materials solution of boundary value problems
What are the methods or approaches for the analytical solutions of boundary value problems in the theory of elasticity for orthotropic materials?
- 188k
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 ...
- 5,546
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 ...
CommunityBot
- 1
0
votes
0
answers
238
views
Simple question on the foundations of spin foam formalism
To make it simple, take the spin foam formalism of ($SU(2)$) 3D gravity. My question is about the choice of the data that will replace the (smoothly defined) fields $e$ (the triad) and $\omega$ (the ...
- 733
3
votes
2
answers
1k
views
Maxwell Stress Tensor and Equations in Mathematician's Language [closed]
In my language, a differential two-form on $\mathbb{R}^4$ (viewed as a differentiable manifold with coordinates $t,x,y,z$) is a differentiable choice at each point of an alternating bilinear function ...
- 52.3k