2
votes
0answers
210 views

Some explanation about Dynin's formalism

I have seen this claim on the Wikipedia page for the Yang-Mills Millenium problem by Alexander Dynin. He is a mathematician working at the Department of Mathematics of Ohio State University and so, I ...
3
votes
0answers
236 views

The dogma of the natural numbers in physics

As is well known "God made the natural numbers; all else is the work of man" (Leopold Kronecker). However, "what would correspond more to the spirit of physics would be a mathematical theory of the ...
0
votes
0answers
102 views

Chain-complex and Co-chain-complex valued Topological Quantum field theories

My research has led to me considering chain-complex and co-chain-complex valued topological quantum field theories. However, I am unable to find any literature that extensively studies this. Is there ...
5
votes
0answers
69 views

Short examples that are/are not quantum-ergodic

Are there any considerably short examples of manifolds that are/aren't quantum ergodic, or quantum unique ergodic? Note that a (compact) Riemannian manifold is said to be quantum ergodic if ...
1
vote
1answer
129 views

Does this Mean Value have a Name?

Question: does the following mean value have a name? $$v^*=\sqrt{\frac{\sum_{i=1}^{n}\alpha_iv_i^2}{\sum_{i=1}^{n}\alpha_i}}, \alpha_i\in\mathbb{R}^+$$ where the $v_i$ are individual speed limits ...
3
votes
1answer
227 views

Electromagnetic duality symmetry

This question arose while reading http://prd.aps.org/abstract/PRD/v13/i6/p1592_1 (Duality transformations of Abelian and non-Abelian gauge fields, by Stanley Deser and Claudio Teitelboim). It is well ...
0
votes
0answers
37 views

Gordon Lemma for Jacobi operators

The Gordon lemma is a useful tool in the theory of 1-D discrete time-independent Schrödinger operators that exploits local repetition in the potential to prove absence of point spectrum. Has anyone ...
10
votes
3answers
402 views

Resource for learning quantum mechanics from the viewpoint of representation theory

Quantum mechanics is deeply connected with representation theory. Therefore, I'm looking for a textbook or article which presents quantum mechanics in a representation theoretic manner. Could anyone ...
8
votes
3answers
404 views

References request: constructive quantum field theory

I am taking a course this semester on QFT, which deals much with constructive quantum field theory. Some of its topics so far involve relationships between non-Gaussian probability measures,Feynman ...
7
votes
2answers
389 views

Kummer's quartic surface and the Dirac operator

The picture shows 1936 photograph by Man Ray of a Kummer surface plaster model in the collection of the Institute Henri Poincare (from Mathematics, Art and Science of the Pseudosphere by Kenneth ...
4
votes
1answer
868 views

Mathematical study of Mpemba effect?

It has been known since the days of Aristotle and Descartes that under certain circumstances warm water freezes faster than cold water. This effect is now commonly known as the Mpemba effect, named ...
7
votes
2answers
252 views

What is the definition of picture changing operation?

What is the definition of picture changing operation? What is a standard reference where it is defined - not just used?
0
votes
0answers
88 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 ...
1
vote
2answers
192 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 ...
3
votes
0answers
100 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 ...
1
vote
0answers
77 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?
3
votes
0answers
285 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? ...
0
votes
1answer
293 views

A reference about Dolbeault cohomology

I am looking for a reference about Dolbeault cohomology when the line bundle is not supposed to be positive.
12
votes
1answer
334 views

Applications of non-separable Hilbert spaces

In applications, Hilbert spaces of interest are often assumed to be separable. In addition to being extremely convenient mathematically, this assumption can often be justified on computational or ...
8
votes
1answer
351 views

Dimensional regularization in odd dimensions

I am not quite sure that my question below is appropriate for this site, probably it should be addressed to the physical commutity. But I hope that some (mathematical) physicists do attend MO. I have ...
2
votes
2answers
161 views

Ewald's generalized theta function

Could anyone provide me some materials on the derivation of Ewald's generalized theta function (in English)? The original paper was written in German :-( Die Berechnung optischer und ...
0
votes
0answers
137 views

Is there a translation invariant measure on an infinite dimensional space 'without points'?

This is just a reference request. I thought I'd come across a paper demonstrating that there is a translation invariant measure on an infinite-dimensional space without 'points' whilst browsing the ...
6
votes
0answers
149 views

Spectral theory for Dirac Laplacian on a funnel

I would like to study the spectral theory of the Dirac Laplacian on a non-compact quotient of the hyperbolic plane by a discrete group (I am particularly interested in the simple case where the ...
4
votes
1answer
119 views

Deriving Helfrich's shape equation for closed membranes

I have a bunch of papers that claim that, from the equation for shape energy: $$ F = \frac{1}{2}k_c \int (c_1+c_2-c_0)^2 dA + \Delta p \int dV + \lambda \int dA$$ one can use "methods of variational ...
3
votes
1answer
127 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 ...
1
vote
1answer
348 views

Partial linearization near a hyperbolic fixed point--Classical scattering

I am currently reading the famous article "Universal Properties of Maps on an Interval" by Collet, Eckmann and Lanford related to the Feigenbaum-Coullet-Tresser universality. I am in particular ...
2
votes
2answers
303 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. ...
2
votes
0answers
102 views

Three body problem with two fermions and a different particle

I'm studying the three body problem with two fermions of unitary mass and another different particle. I need references of the HVZ theorem in this case. Is there someone who knows them?
4
votes
2answers
821 views

Eigenvalues of random Hamiltonian matrices

A real $2n\times 2n$ Hamiltonian matrix has the general form $$H=\begin{pmatrix} A & B \cr C & -A^T \end{pmatrix} $$ where $A$, $B$ and $C$ are $n\times n$ matrices, and $B$ and $C$ are ...
6
votes
7answers
608 views

Quantization of a classical system (e.g. the case of a billard)

There has been already several questions asking for an introduction to quantum mechanics for a mathematician, but this ons is slightly different, and more restrictive. I know (some) quantum mechanics, ...
11
votes
2answers
753 views

Hopf Algebra for a physicist

Hello, for my bachelor's thesis I need to understand the Hopf Algebra of Feynman Diagrams. As I have only litte knowledge in Algebra by now I wanted to ask where I could start and what preknowledge I ...
4
votes
3answers
587 views

Meaning of a phrase from “The algebra of grand unified theories”.

Motivated by an answer to this mathoverflow question I've been making an effort to understand Baez and Huerta's article "The algebra of grand unified theories". As far as I can tell, mathematically, ...
4
votes
0answers
111 views

FRT construction in the case of super algebras

I'm looking on papers which are talking about the super quantum algebra osp(2|1). I want to understand how one applies the FRT construction in the case of osp(2|1). Of course there is a super ...
1
vote
0answers
118 views

Rigid-body in a central field: orbital and attitude motion

Question I would like to find a nice set of explicit coordinates for the family (parametrised by angular momentum) of reduced systems representing a rigid-body in a central field in which the orbital ...
1
vote
0answers
231 views

Properties of Clifford Algebras

It is a well known fact that Clifford algebras, $Cl(p,q)$, have similar properties depending on $(p-q)\mod 8$. In most of the places I have found a proof of the theorem, explicit representations of ...
1
vote
0answers
58 views

Random Schrödinger operators with asymmetric Lifshitz tails?

For a quantum mechanical system with a periodic Hamiltonian (Schrödinger operator) $H$, let $N(E)$ be its integrated density of states, i.e. the fraction of eigenvalues in the spectrum $\sigma(H)$ ...
4
votes
1answer
247 views

Work on an Einstein-Hilbert type action but with the *absolute value* of scalar curvature?

This is only my second question on mathoverflow, so my apologies if this would be more appropriate at a physics site. My question concerns a modification to the Einstein-Hilbert action. The standard ...
2
votes
0answers
99 views

Concerning the classification of transversally integral affine structures on symplectic foliations $F$

Recently, in http://arxiv.org/pdf/1207.3655.pdf, the authors have determined that an element $c$ in $H^2(P, P_v)$ is the Chern class of a twisted isotropic realization $p$: $(M, ...
1
vote
1answer
248 views

Stieltjes convolution with white noise

I'm looking for a reference that would discuss a Stieltjes convolution between a wiener process and a function of bounded variation. Additionally, I had a question about this sort of convolution. Is ...
5
votes
1answer
237 views

Where can I read about exponential sums corresponding to Jones Polynomial?

I remember reading that a number theoretic analogue of Witten's path integral formula for the Jones polynomial: $$\text{Jones}_K(e^{2\pi i/(k+2)})=\int_{\text{$SU(2)$ connections on $\mathbb ...
3
votes
1answer
351 views

Turing machines and Ising model

I have currently started a new research line aiming to prove a mapping between a 2-symbol Turing machine and the one dimensional Ising model. The connection is seen by recognizing that a set of ...
8
votes
2answers
337 views

What is the physical difference between states and unital completely positive maps?

Mathematically, completely positive maps on C*-algebras generalize positive linear functionals in that every positive linear functional on a C*-algebra $A$ is a completely positive map of $A$ into ...
3
votes
0answers
158 views

Krichever-Novikov-Dubrovin description for not-algebraic spectral curve

Non-algebraic curves play an increasing role in string theory, sometimes they are known to be related to the integrable systems of the KP/Toda type. Are there any investigated examples of the ...
4
votes
1answer
504 views

How the Jacobi metrics may be useful in mechanics with or without constraints?

A mechanical system $(Q,K,V)$ is specified by the configuration space $Q,$ the potential energy $V\in C^\infty(Q),$ and the kinetic energy $K=K_g$ given by a Riemannian metric $g$ on $Q.$ If ...
3
votes
0answers
114 views

SOS model - height

Let $\Lambda_n = \{ -n,\ldots,n\}^2$ and let $\{X_i\}_{i\in \Lambda_n}$ be the family of $\mathbb{R}$-valued of random variables with the density proportional to $\exp(-\sum_{i\sim j} |X_i - X_j|),$ ...
8
votes
4answers
765 views

References for classical Yang-Mills theory

I am looking for a reference to study classical (i.e., not quantized) Yang-Mills theory. Most of the sources I find focus on mathematical aspects of the theory, like Bleecker's book Gauge theory and ...
21
votes
3answers
2k views

Shape of snowflakes

Is there a mathematical theory that explains the shape of a snowflake? Why is it not round? Update Tree-like metric spaces appear often as limits of sequences of metric spaces (say, asymptotic cones ...
1
vote
1answer
318 views

Reference request: Seminal papers in gauge-theoretic mathematics [closed]

Following on from previous question I was also searching for seminal papers in gauge theory. Would be greatly appreciative of references to such.
4
votes
2answers
483 views

Reference request: Introductions to current mathematics derived from / related to gauge theories

I was searching for introductions to current mathematics related to gauge theories. Can someone suggest some good references? E.g. Topics in Physical Mathematics by K. Marathe
8
votes
5answers
917 views

Is there a relation between 4-dimentional general relativity and exotic smooth structures on $\mathbb{R}^4$?

Let's say General Relativity is the study of the Einstein equation on smooth Lorentzian manifolds, i.e. pseudo-Riemanniann manifolds of signature $(n-1,1)$. I've heard more than once people say that ...