**5**

votes

**0**answers

132 views

### Energy barriers between Hadamard matrices

Hadamard matrices may be characterized as $n\times n$ real orthogonal matrices $U$ that achieve the lowest possible "energy" as defined by the (scaled and shifted) entry-wise 1-norm:
$$
E(U)=n^2 ...

**0**

votes

**0**answers

77 views

### Master Equation to Fokker-Planck for a Jump-Diffusion

Does anyone know if there is a derivation of the Master Equation approximation by a Kolmogorov backward equation (Fokker-Planck) to a jump-diffusion with a compensated Poissonian integral? If not, can ...

**2**

votes

**0**answers

125 views

### How to perform this matrix integral?

Edit: some backgrouds added.
In quiver matrix model which is reviewed DV or CKR, the path integral reduce to the matrix integral
$$Z \sim \int \prod_{i=1}^r d\Phi_i \prod_{<a,b>} dQ_{ab} ...

**0**

votes

**1**answer

202 views

### On the Geroch's argument

During the study of Geroch's argument to prove positive mass theorem, I faced a problem explained below:
Suppose $(M,g_{\mu \nu})$ is a four dimensional Lorentzian Manifold and $\Sigma$ is a ...

**1**

vote

**2**answers

190 views

### Positivity of the Coulomb energy in two dimensions

In dimensions $d\geq 3$ the Coulomb energy is always non-negative (since the Fourier transform of $\frac{1}{|\cdot|^{d-2}}$ is non-negative). What can one say about positivity properties of the ...

**2**

votes

**1**answer

184 views

### Probability measures on $L^p$

Let $(X,\mathcal X,\mu)$ be a fixed measure space, and suppose that $\mu$ is stationary and ergodic with respect to the (left) action of a topological group $G$. Stationarity means that $\mu = g_* \mu ...

**2**

votes

**1**answer

152 views

### Question about the Aganagic-Vafa A-brane

According to Aganagic-Vafa (hep-th/0012041) and Fang-Liu (arXiv:1103.0693), for a semi-projective toric Calabi-Yau 3-manifold $X$, the Aganagic-Vafa A-brane $L_{AV}\subset X$ is defined by the ...

**6**

votes

**1**answer

192 views

### Understanding the intermediate field method for the $\phi^4$ interaction

In Rivasseau's and Wang's How to Resum Feynman Graphs, on page 11 they illustrate the intermediate field method for the $\phi^4$ interaction and represent Feynman graphs as ribbon graphs. I had to ...

**1**

vote

**2**answers

477 views

### Uniqueness on square root of complex Line Bundle

Let $L$ be a line bundle over a compex manifold $X$, a square-root of $L$ is a line bundle $M$ such that $M^{\otimes2}=L$. My question is when the square-root of Line Bundle is unique?

**3**

votes

**0**answers

95 views

### Where is there a treatment of double field theory other than in local coordinates?

The n-lab seems to lack a treatment of double field theory. Where is there a treatment other than in local coordinates? Or at least one which identifies the coordinates as local coordinates for a ...

**0**

votes

**1**answer

157 views

### direct proof that schrodinger's equation kernel corresponds to delta-function initial value [closed]

I want to show directly, that the kernel for the n-dimensional free linear schrodinger equation, if taken to time t=0, is dirac's $\delta $ function. I can show that the integral is constant, but it ...

**4**

votes

**1**answer

327 views

### Quantization of symplectic vector space and choice of lagrangian subspaces

My question is related to Geometric Quantization.
I don't undrestand the philosophy of following assertion
If $(V,\omega)$ be a symplectic vector space then the quantizations of
$V$ ...

**2**

votes

**0**answers

164 views

### Looking for good conferences / workshops on applications of renormalization group methods [closed]

I am looking for conferences and/or workshops, where people working on different problems using renormalization group methods come together to share their results and experience.
As I have noted, ...

**1**

vote

**0**answers

107 views

### Brownian particles in a box: the probability that a sphere (of some radius) centered on a particle only contains one particle for a duration of time

Imagine I have a set of $(s_1,...,s_N) \in S$ Brownian particles in a box of sidelength $L$, each with the same coefficient of diffusion $D$. We fix one particle at the center of the box, and draw a ...

**28**

votes

**5**answers

727 views

### are there natural examples of classical mechanics that happens on a symplectic manifold that isn't a cotangent bundle?

I'm curious about just how far the abstraction to a symplectic formalism can be justified by appeal to actual physical examples. There's good motivation, for example, for working over an arbitrary ...

**3**

votes

**0**answers

83 views

### What does the renormalization group flow corresponding to a turbulent subrange with a broad band forcing look like?

In a renormalization group analysis of turbulent flows, such as for example done by Barbi and Münster here who derive an action for the Navier-Stokes equations, insert it into the Wilson equation, and ...

**3**

votes

**0**answers

197 views

### Looking for a necessary and sufficient condition for the polarization $\mathbb{P}$ being positive

My question is about positivity of polarization in Geometric quantization theory. Let $\mathbb{P}$, be a complex polarization on symplectic manifold $(M,\Omega)$. For every $m\in M$, we can define a ...

**0**

votes

**1**answer

274 views

### Symplectic structure on $Sym^kG^{\mathbb{C}} $

Let $G$ be a compact Lie group, and let $G^\mathbb{C}$ be its complexification.
I am looking for a symplectic structure (without use of coordinates) on
$$
Sym^kG^{\mathbb{C}},
$$
PS:Here ...

**2**

votes

**1**answer

320 views

### looking for an identity for higher jet bundle $J^kM$?

We know this fact that the first jet Bundle $J^1M$ is diffeomorphic with $T^*M×\mathbb{R}$.i.e,
($J^1M=T^*M×\mathbb{R}$)
Is there something like this identity for higher jet bundle $J^kM$?
I editted ...

**4**

votes

**0**answers

195 views

### Local version of a slice (for a Lie group action)

Let $\Upsilon: G \times M \to M$ be a smooth action of a Lie group $G$ on a manifold $M$.
Isenberg and Marsden (1982) define a slice at $m \in M$ as a submanifold $S \subseteq M$ containing $m$ such ...

**1**

vote

**1**answer

312 views

### pre-quantization of Jet bundle

We know that the notion of Jet bundle $J^kM×\mathbb{R}$, is generalization of cotangent bundle. What is the prequantization of $J^kM×\mathbb{R}$?

**5**

votes

**0**answers

135 views

### Density of odd and even eigenstates of an integral operator

Consider an integral operator $(Kf)(x)=\int_{-1}^{1}K(x-y)f(y)dy$, where the kernel $K(-x)=K(x)$ is an even function.
Let $\lambda_n$ be the ordered eigenvalues of $K$ and $f_n(x)$ the ...

**1**

vote

**0**answers

76 views

### H-flux by any other name

There are more than a few papers referring to H-flux and/or H-twist etc.
Is there anywhere a survey relating these variants?

**2**

votes

**0**answers

186 views

### a question about geometric quantization background

I don't understand why for geometric description of a regular system, we take always the classical phase space as a symplectic manifold?

**3**

votes

**0**answers

240 views

### A gentle introduction to CFT [closed]

1) Which is the definition of a conformal field theory?
2) Which are the physical prerequisites one would need to start studying conformal field theories?
(i.e Does one need to know supersymmetry? ...

**8**

votes

**4**answers

562 views

### Can the equation of motion with friction be written as Euler-Lagrange equation?

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 ...

**3**

votes

**1**answer

151 views

### Does fixing the reparameterization invariance of the string action correspond to some kind of orbifolding?

Does fixing the reparameterization invariance of the string action, for example by choosing the light-cone gauge
$$
X^{+} = \beta\alpha' p^{+}\tau
$$
$$
p^{+} = \frac{2\pi}{\beta} P^{\tau +}
$$
...

**4**

votes

**1**answer

76 views

### Understanding the diffraction limit in the context of being provided perfect information on an intensity distribution

As per http://scienceworld.wolfram.com/physics/AiryDisk.html, let the intensity distribution given by diffraction around a circular aperture be proportional to:
$I(r) \propto [\frac{J_1(r)}{r}]^2$
...

**5**

votes

**0**answers

247 views

### Why does closed string theory have only one dilaton field instead of $22$?

Looking at $5D$ Kaluza-Klein theory, the Kaluza-Klein metric is given by
$$
g_{mn} = \left(
\begin{array}{cc}
g_{\mu\nu} & g_{\mu 5} \\
g_{5\nu} & g_{55} \\
\end{array}
\right)
$$
...

**8**

votes

**5**answers

282 views

### Observables and dimensional analysis

Here is a simple question about physical units that I hope has a simple satisfying answer. In mathematically sophisticated treatments of both quantum and classical physics one often speaks of an ...

**1**

vote

**1**answer

158 views

### What's the asymptotic behavior of this function at large distance? [closed]

This question is based on some Physics motivation. Define a distance function $f(\mathbf{r})=\int_{\Omega }d^2k\int_{\Omega }d^2q \cos[(\mathbf{k}-\mathbf{q})\cdot\mathbf{r}]$, where ...

**7**

votes

**0**answers

182 views

### The space-time dimension of the N-superstring theory?

Let $\mathfrak{W}$ be the Lie algebra generated by $d_{n} = ie^{in\theta}\frac{d}{d\theta}$ and $\mathfrak{Vir} = \mathfrak{W} \oplus C \mathbb{C}$ its central extension:
$$
...

**5**

votes

**0**answers

162 views

### Are there exactly solvable CFTs?

I am wondering if there are CFTs such that n-point correlation functions in them of the fields (may be the primaries or of some notion of twist fields) is exactly known.
Are there such?
Aren't ...

**0**

votes

**0**answers

77 views

### N=2 Dualities; k-differentials on the riemann sphere and spectral curves

Currently I am working on my masters thesis about dualities in QFT and their geometric realizations.
As of now, I am trying to understand the article 'N=2 Dualities" by Davide Gaiotto. On the internet ...

**11**

votes

**1**answer

770 views

### Is this error in this paper of Langlands fixable?

The FQS criterion for the Virasoro algebra was discovered by Friedan, Qiu and Shenker (1), but the mathematicians found their proof insufficient, so that, FQS (2) and Langlands (3), published in the ...

**2**

votes

**1**answer

115 views

### Absent 2nd order terms in deformation quantization of Poisson manifolds

I am reading Kontsevich' famous paper on deformation quantization of Poisson manifolds. In section 1.4.2 on page 4 he gives the general formula for the star product associated to a Poisson structure ...

**2**

votes

**1**answer

357 views

### A question about flag variety of $SL(n,\mathbb{C})$

We know that the flag variety $SL(2,\mathbb{C})/B$ which $B$ is Borel subgroup, can be identified with $\mathbb{P^1}$, What can we say about $SL(n,\mathbb{C})/B$ which $B$ is Borel subgroup of ...

**5**

votes

**1**answer

156 views

### How does one calculate homotopy classes for group coset spaces?

Inspired by Witten's Wess-Zumino term arguments, I'm curious to know how one calculates homotopy classes more generally for coset spaces. In the above example the coset is $G/H=(SU(3)_L\times ...

**7**

votes

**1**answer

246 views

### Calogero-Moser system: relationship between dual variables and the KKS construction

This is a question about the relationship between two ways of viewing the Calogero-Moser system.
$$\ddot x_i=2\sum_{j\neq i}\frac{1}{(x_i-x_j)^3}\qquad i=1,\ldots N$$
By introducing the $N$ ...

**51**

votes

**1**answer

3k views

### What is the amplituhedron?

The paper ”Scattering Amplitudes and the Positive Grassmannian” by Nima Arkani-Hamed, Jacob L. Bourjaily, Freddy Cachazo, Alexander B. Goncharov, Alexander Postnikov, and Jaroslav Trnka, introduces ...

**16**

votes

**1**answer

568 views

### Combinatorial spin structures

I would like to know how to define spin structures combinatorially, for an oriented smooth manifold equipped with a triangulation. In the case of a 2d manifold, spin structures correspond to ...

**2**

votes

**0**answers

61 views

### What are the boundary asymptotics of harmonic symmetric transverse traceless rank-s tensors on $\mathbb{H}^n$ in the Poincare upper-half-space model? [closed]

This question is motivated by the results in this paper, http://calvino.polito.it/~camporesi/JMP94.pdf
In this paper some of its most important results about the asymptotics of symmetric traceless ...

**4**

votes

**1**answer

304 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 ...

**0**

votes

**1**answer

120 views

### How to calculate eigenvalue density function of $XX^\dagger$ from the density function of X

Let X be a complex random matrix, which has the probability function (drawn from the ensemble) V($XX^\dagger$), where V(x) is some function which guaranties good behavior at infinity. Note the unitary ...

**2**

votes

**0**answers

92 views

### Positiveness of the double integral

How it can be proved that the following double integral (which emerged in a physics project) $$\int\limits_{-1}^1d\tau\;\tau \int\limits_0^\infty dk\frac{k\sin{(kr\tau)}}{(1+\beta ...

**2**

votes

**0**answers

79 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 $(s_1,s_2,...,s_n)$ ...

**4**

votes

**1**answer

288 views

### 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 ...

**6**

votes

**1**answer

221 views

### Formal series convergence in deformation quantization and $C^*$-condition

A link between formal series convergence in deformation quantization (strict deformation quantization) and producing $C^*$-algebras instead of mere $*$-algebras (which ...

**1**

vote

**1**answer

513 views

### An integral representation of the Riemann zeta function

I am referring to the equality in equation $3.29$ (page 12) and $4.20$ (page 17) in this paper.
I am unable to recognize where this comes from or what is the general expression for values other than ...

**5**

votes

**2**answers

263 views

### Physical meaning of the integral cohomology condition in Souriau-Kostant pre-quantization?

The question is in the title. The form of the condition looks like the Bohr-Sommerfeld quantization formula of angular momentum, is there a link between the two formulas?