Questions tagged [mp.mathematical-physics]

Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.

Filter by
Sorted by
Tagged with
4 votes
0 answers
208 views

Open-closed string correspondence

Recently, after many years of searching for the right source, I came across the excellent lecture by Aspinwall, "Some Applications of Commutative Algebra to String Theory", in Eisenbud's Festschrift. ...
user6419's user avatar
  • 431
38 votes
4 answers
4k views

A family of polynomials whose zeros all lie on the unit circle

I had posted the following problem on stack exchange before. Suppose $\lambda$ is a real number in $\left( 0,1\right)$, and let $n$ be a positive integer. Prove that all the roots of the ...
math110's user avatar
  • 4,230
5 votes
0 answers
100 views

Paving property

In their famed paper (https://arxiv.org/abs/math-ph/0011053), Bourgain and Goldstein conjecture what they call the paving property: Let $H_{jk}=\delta_{j,k+1}+\delta_{j,k-1}+v(\theta+j\omega)\delta_{...
Eduard Tetzlaff's user avatar
4 votes
0 answers
321 views

Topological field theories and their path integrals

Examples of topological field theories are the cohomological field theories as they were initially defined by Witten [1]. Such examples include the Donaldson-Witten theory in 4d or the Gromo-Witten ...
Gorbz's user avatar
  • 651
0 votes
0 answers
117 views

Barnes's double $\Gamma$-function, $\gamma_{h}(0) = -\frac{1}{12}$?

I apologize if I may have gotten the name of the function incorrectly. The function $\gamma_h(x)$ is defined in Appendix A of the paper SEIBERG-WITTEN THEORY AND RANDOM PARTITIONS, https://arxiv.org/...
user113988's user avatar
1 vote
0 answers
78 views

Finite sum of spherical Bessel functions

In L.G. Afanasyev, A.V. Tarasov, Breakup of relativistic pi+pi- atoms in matter, Phys. At. Nucl. 59 (1996) 2130 the following identity is given for the spherical Bessel functions $j_n(z)=\sqrt{\frac{\...
Zurab Silagadze's user avatar
0 votes
0 answers
151 views

Physical significance of some killing vector fields on a $G_2$ manifold

I have recently calculated three linearly independent Killing vector fields on a G^2 manifold with a specific metric, which can be found in this paper: https://arxiv.org/pdf/hep-th/0011256.pdf The ...
user avatar
6 votes
1 answer
1k views

Question on Witten’s paper “Supersymmetry and Morse theory”

EDIT. I am trying to read the article “Supersymmetry and Morse theory” by E. Witten (JDG 17 (1982)). This well known article applies some tools developed by physicists (e.g. path integrals) to ...
asv's user avatar
  • 21.1k
3 votes
0 answers
160 views

Nekrasov Partition function and the leading term of Prepotential

I've got a pretty basic question from the paper SEIBERG-WITTEN THEORY AND RANDOM PARTITIONS, https://arxiv.org/pdf/hep-th/0306238.pdf. In (4.25) the author expressed the partition function ...
user113988's user avatar
3 votes
1 answer
230 views

Casimir force without cheating

If memory serves me right, some years ago I heard rumors about developing methods of computing the Casimir force which are rigorous (by the standards of constructive quantum field theory). I ...
Alex Gavrilov's user avatar
1 vote
0 answers
99 views

Which operators constructed from 10d gamma matrices commute with $SO(1,2)\times SO(3)\times SO(3)$?

In the paper Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory by Gaiotto and Witten, an in-depth analysis of boundary conditions in N=4 Super Yang-Mills in four dimensions in ...
Mtheorist's user avatar
  • 1,135
2 votes
3 answers
498 views

Graph of a Lie super algebra

Let $A$ be a generalized Cartan matrix and let $\mathfrak{g}$ be the Kac-Moody Lie algebra associated to $A$. There is an associated graph of $\mathfrak{g}$ which is known as the Dynkin diagram of $\...
GA316's user avatar
  • 1,219
0 votes
1 answer
103 views

Does Helmholtz's decomposition give an over-determined rotational flow?

From Helmholtz's decomposition, $v=v_{\scriptscriptstyle IR} +v_{\scriptscriptstyle R} $ where $\nabla\times v_{IR} =0$ and $\nabla\cdot v_R=0$ when apply this to the linearized Navier-Stokes ...
Huang Wei's user avatar
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 ...
Abhijeet Melkani's user avatar
3 votes
0 answers
142 views

Frobenius structure for A_n singularities

I need to compute monodromy matrices $M(v)$, associated to a Frobenius structure for $A_n$ singularity with flat coordinates $v_1,\dots,v_n$, that is, $f(x)=x^{n+1}$. (due to Saito, Dubrovin etc.) ...
Krieg899's user avatar
3 votes
1 answer
213 views

A problem about closed 2-forms on Minkowski space

The problem is: For any closed 2-form in the Minkowski space $\mathbb{R}^{3,1}$ satisfiying $dF=0$ and $\delta F \ne 0$ (with $\delta$ denoting the codifferential), does there exist a Lorentz ...
jacktang1996's user avatar
3 votes
2 answers
405 views

References on thin film equation: derivation and properties

Where can I find a derivation of the thin film equation $$u_t = - \mathrm{div} (u^m\nabla\Delta u)$$ from a physical model? a good introduction to its properties (e.g. conserved quantities and ...
user avatar
9 votes
1 answer
895 views

Fedosov vs. Kontsevich deformation quantization : a beginner survey

I'm a condensed matter physicist who tries to understand the details of deformation quantization. In my self-made training, I've found two huge pieces of work, namely Fedosov, B. V. (1994). "A ...
FraSchelle's user avatar
0 votes
0 answers
80 views

How to calculate the exact probability $p$ at which maxima occurs in the curves in an infinite system?

I'm writing with respect to this paper: Khatun, Dutta, and Tarafdar - "Islands in Sea" and "Lakes in Mainland" phases and related transitions simulated on a square lattice Here's a ...
user avatar
2 votes
0 answers
101 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 ...
user avatar
13 votes
0 answers
329 views

A modified Heisenberg uncertainty relation

Let $\psi\colon\mathbb R\to\mathbb C$, and set $$ F[\psi]:=\pi\ \frac{\displaystyle\int_{\mathbb R} |x|\;|\psi(x)|^2\,\mathrm dx}{\displaystyle\int_{\mathbb R}|\psi(x)|^2\,\mathrm dx}\frac{\...
AccidentalFourierTransform's user avatar
1 vote
0 answers
262 views

Integral involving square of associated Laguerre polynomial and sperical bessel function

In a quantum mechanical problem I encountered the integral $$I_k=\int_0^\infty x^{2(l+1)-k}j_k(\sigma x)e^{-x}[L_{n-l-1}^{2l+1}(x)]^2 dx,$$ where $j_k(x)$ is a spherical Bessel function, and $\sigma$ ...
Zurab Silagadze's user avatar
3 votes
1 answer
160 views

How to show that a map which relates to Donaldson–Thomas invariants is an automorphism?

I am reading the lecture notes INTRODUCTION TO DONALDSON–THOMAS INVARIANTS. I have a question in the end of page 1 about the proof of a map is an automorphism. Let $m>0$ be an integer. Let $\...
Jianrong Li's user avatar
  • 6,101
5 votes
0 answers
245 views

Localization principle in integration over supermanifolds

This post is closely related to the post Localization principle in supersymmetry and can be considered as a continuation of it, although independent. In § 9.3 of the book "Mirror symmetry" (K. Hori ...
asv's user avatar
  • 21.1k
3 votes
1 answer
228 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....
sadiaz's user avatar
  • 402
0 votes
0 answers
117 views

Green's third identity potential massive object

Consider a massive object occupying a volume $U$ with boundary $\partial U$. Let the gravitational potential inside be $V_{in}$ and outside $V_{out}$ Normally the gravitational field of a massive ...
Matt Majic's user avatar
6 votes
0 answers
372 views

What’s the limit of a vector bundle?

In geometric measure theory, there’s an answer to the question “what’s the limit of a family of submanifolds”, namely there’s some kind of object called an integral current. In the geometric ...
Vivek Shende's user avatar
  • 8,663
2 votes
1 answer
418 views

$SO(6) \to SU(2) \times SU(2) \times U(1)$ branching rules

What do these branching rules mean? \begin{eqnarray*} SO(6)_E &\to& SU(2)_\ell \times SU(2)_r \times U(1)_\Sigma \end{eqnarray*} I am taking these examples from a paper of Gukov (on p.51) ...
john mangual's user avatar
  • 22.6k
1 vote
1 answer
694 views

Invariance of a vector under parallel transport along an infinitesimal orthogonal loop

I'm not very familiar with differential geometry and am coming from a general relativity background, so would appreciate help with a question from that context. If this question could be posed in a ...
Aegon's user avatar
  • 173
1 vote
0 answers
141 views

Why is $\textbf{J}$ called angular momentum?(Quantum) [closed]

Why is $\textbf{J}$ called angular momentum operator? Can anyone explain why the expectation value of J is angular momentum? Here is how $\textbf{J}$ is defined: The rotation operator $$ U(\alpha)=\...
user avatar
1 vote
0 answers
60 views

Numerical computation of spectrum for operators on real line with "confining potential"

I am looking to understand the conditions under which one can expect "reasonably" accurate solution to leading eigenvalues/eigenvectors of a second order differential operator posed on the real line. ...
mystupid_acct's user avatar
8 votes
1 answer
469 views

Reference request: Partition function as a topological invariant of a QFT

I have read (mainly in the articles of Atiyah) that the partition function is the simplest topological invariant of a quantum field theory. I have an arithmetic geometry background and know ...
Dimitri's user avatar
  • 93
0 votes
0 answers
82 views

Euclidean or Minkowski Metric for Clustering Spatio-Temporal Data?

Question: when does using Minkowski metric $\quad\sqrt{x^2+y^2+z^2-t^2}\quad $for clustering $(x,y,z,t)$ data yield better results than using Euclidean metric $\quad\sqrt{x^2+y^2+z^2+t^2}\ $? I ...
Manfred Weis's user avatar
  • 12.6k
3 votes
1 answer
144 views

Does the Leclerc-Thibon involution exchange vertex operators of the first and second type?

This question is about $U_q ( \hat{\mathfrak{sl}}_2 )$ representation theory. There is a notion of vertex operators $\Phi_{\pm }(z)$ of first and $\Psi_{\pm}(z)$ of the second type. They are defined ...
quinque's user avatar
  • 375
12 votes
3 answers
437 views

Geometrically quantizing real Grassmannians

It seems that the Grassmannian of oriented 2-dimensional planes in $\mathbb{R}^n$ $$ \mathrm{Gr}(n,2) = \frac{\mathrm{SO}(n)}{\mathrm{SO}(n-2) \times \mathrm{SO}(2)} $$ has a symplectic structure ...
John Baez's user avatar
  • 21.3k
3 votes
2 answers
540 views

Can one obtain this ODE as an Euler-Lagrange equation?

Some of the second order ODE can be considered as Euler-Lagrange equations for an appropriate Lagrangian. However this is true not for arbitrary second order equation. But some of important equations ...
alexa's user avatar
  • 43
2 votes
0 answers
107 views

How exactly are holomorphic maps with hyperkahler targets identified as triholomorphic maps?

In Appendix A of Hyperinstantons, the Beltrami Equation, and Triholomorphic Maps by Fre et al., it is described how holomorphic maps from a Riemann surface to a hyperkahler manifold $\mathcal{N}$, ...
Mtheorist's user avatar
  • 1,135
6 votes
1 answer
214 views

Possibly new solution to equal-mass three-body problem; refinement required

(This is a repost of this question from 18 months ago on the main Mathematics SE site, as the response there has been underwhelming, and I thought here would be a better authority. As you can probably ...
404UserNotFound's user avatar
6 votes
0 answers
196 views

A 'Fock'-type construction on a $C^*$-algebra

In very rough terms, let $A$ be a complex unital $C^*$-algebra. Assume it nuclear for convenience, but it doesn't matter much. Consider the 'Fock'-type $C^*$-algebra (don't know a better name for it) $...
Bedovlat's user avatar
  • 1,939
6 votes
1 answer
342 views

Toda Hierarchy and Quantum Cohomology of $\mathbb{P}^1$ Frobenius manifolds

People usually say that the quantum cohomology of $\mathbb{P}^1$ Frobenius manifold $QH^*(\mathbb{P}^1)$, corresponds to dispersionless extended Toda hierarchy (e.g. page 6 of https://arxiv.org/pdf/...
user113988's user avatar
3 votes
0 answers
79 views

Generalisation of Lyapunov time to stochastic dynamical systems

Might there be useful generalisations of the Lyapunov time to stochastic dynamical systems? In particular, I'm interested in methods for calculating confidence intervals around stochastic analogues of ...
Aidan Rocke's user avatar
  • 3,827
17 votes
3 answers
3k views

What is an "Instanton" in classical gauge theory? (to a mathematician)

There's already a question about the same topic but I think its aim is different. Classical (non-quantum) gauge theory is a completely rigorous mathematical theory. It can be phrased in completely ...
Saal Hardali's user avatar
  • 7,549
8 votes
0 answers
280 views

Lax pairs in an abstract formalism

I am reading Integrals of Nonlinear Equations of Evolution and Solitary Waves by Peter Lax and I'm having a hard time. The methods are pioneering, of course, but Lax does not bother much to provide ...
Delio Mugnolo's user avatar
60 votes
4 answers
5k views

Is there a mathematical and information theoretic explanation for this cube packing phenomenon?

I saw this unintuitive result on dice packing: A jumble of thousands of cubic dice, agitated by an oscillating rotation, can rapidly become completely ordered, a result that is hard to produce with ...
Turbo's user avatar
  • 13.7k
4 votes
1 answer
459 views

an application of nth moment of Poisson distribution with stirling number

I was reading the paper on arixv. I was confused the equation of nth moment of Poisson distribution. The detail and partial paper as follow: ... For large N, this connection probability takes ...
Nick Dong's user avatar
  • 211
0 votes
0 answers
65 views

How to Evaluate the ABJM partition function for N=2

This is the ABJM partition function on the 3-sphere, $$ Z(2) = \int \frac{d^2\mu}{(2\pi)^2} \frac{d^2\nu}{(2\pi)^2} \frac{\left[ 2 \sinh \frac{\mu_1 - \mu_2}{2}\right]^2\left[ 2 \sinh \frac{\nu_1 - \...
john mangual's user avatar
  • 22.6k
14 votes
1 answer
720 views

For a stable matrix $B$ and anti-symmetric $T$, such that $B(I+T)$ is symmetric, show that $\mbox{tr}(TB)\leq0$

Let stable matrix (i.e., its eigenvalues have negative real parts) $B \in \mathbb R^{n \times n}$ and anti-symmetric matrix $T \in \mathbb R^{n \times n}$ satisfy $$B^\top - T B^\top = B + B T$$ ...
stochastic's user avatar
1 vote
0 answers
84 views

Particle density in phase space normalization under proliferation

Consider $1,..,N$ indistinguishable particles in $\mathbb{R}^2$ and let them evolve according to a brownian motion and proliferation. Let $u: \mathbb{R}_+ \times \mathbb{R}^2 \rightarrow \mathbb{R}_0^+...
Jack_Stiller10's user avatar
7 votes
1 answer
424 views

Naturally occuring counting process with a 1/log asymptotics?

Besides prime numbers, is there another physically realizable counting process that exhibits a 1/log density ? The reason I am posting this question is that we are measuring the response of a quantum ...
shantanu's user avatar
47 votes
2 answers
4k views

The two ways Feynman diagrams appear in mathematics

I've heard about two ways mathematicians describe Feynman diagrams: They can be seen as "string diagrams" describing various type of arrows (and/or compositions operations on them) in a monoidal ...
Simon Henry's user avatar
  • 39.9k

1
16 17
18
19 20
43