Tagged Questions
7
votes
2answers
2k views
Some Korean researchers saying that they solved Yang-mill existence and mass gap problem
Today, Korean media is reporting that a team of South Korean researchers solved Yang-Mill existence and mass gap problem. Did anyone outside Korea even notice this? I was not able to notice anything ...
3
votes
1answer
79 views
Transformation law for fermionic measure in functional integral
I am reading the paper "Bosonization in a Two-Dimensional Riemann-Cartan Geometry", Il Nuovo Cimento B Series 11
11 Marzo 1987, Volume 98, Issue 1, pp 25-36, ...
1
vote
2answers
160 views
How much pure math should a physics/microelectronics person know [duplicate]
I do condensed matter physics modeling in my phd and I was struck up learning quite an amount of physics. But while having done lot of physics courses, I see that if I learn pure math I would ...
4
votes
0answers
67 views
Electric potential of a spheroidal gaussian
I'm looking for results that compute the electrostatic potential due to a spheroidal gaussian distribution. Specifically, I'm looking for solutions of equations of the form
$$
...
8
votes
1answer
331 views
Schwinger representation of operators for n-particle 2-mode symmetric states
A bosonic (i.e. permutation-symmetric) state of $n$ particles in $2$ modes can be written as a homogenous polynomial in the creation operators, that is
$$\left(c_0 \hat{a}^{\dagger n} + c_1 ...
6
votes
1answer
110 views
precise definition of “moduli space”
I'm curious what the precise definition of the moduli space of a QFT is. One often talks about the classical moduli space, which then can get quantum corrections. Does this mean the quantum moduli ...
6
votes
2answers
91 views
fitting free QFTs into the Haag-Kastler algebraic formulation
Has the free Klein-Gordon quantum field theory been fitted into the
Haag-Kastler algebraic framework? (Actually, John Baez told me "yes", and he should know.) If so, can you describe the basic
...
18
votes
1answer
286 views
Geometric picture behind quantum expanders
A $(d,\lambda)$-quantum expander is a distribution $\nu$ over the unitary group $\mathcal{U}(d)$ with the property that: a) $|\mathrm{supp} \ \nu| =d$, b) $\Vert \mathbb{E}_{U \sim \nu} U \otimes ...
4
votes
1answer
34 views
Tip of a spreading wave-packet: asymptotics beyond all orders of a saddle point expansion
This is a technical question coming from mapping of an unrelated problem onto dynamics of a non-relativistic massive particle in 1+1 dimensions. This issue is with asymptotics dominated by a term ...
11
votes
2answers
70 views
Discussions of the axioms of AQFT
The most recent discussion of what axioms one might drop from the Wightman axioms to allow the construction of realistic models that I'm aware of is Streater, Rep. Prog. Phys. 1975 38 771-846, ...
7
votes
1answer
88 views
Fourier Methods in General Relativity
I am looking for some references which discuss Fourier transform methods in GR. Specifically supposing you have a metric $g_{\mu \nu}(x)$ and its Fourier transform $\tilde{g}_{\mu \nu}(k)$, what does ...
6
votes
1answer
158 views
Thermodynamic limit “vs” the method of steepest descent
Let me use this lecture note as the reference.
I would like to know how in the above the expression (14) was obtained from expression (12).
In some sense it makes intuitive sense but I would ...
6
votes
3answers
759 views
Interesting topics to research in mathematical physics for undergraduates
I'm planning on getting into research in mathematical physics and was wondering about interesting topics I can get into and possibly make some progress on.
I'm particularity fond of abstract algebra ...
9
votes
4answers
295 views
Applications of Geometric Topology to Theoretical Physics
Geometric topology is the study of manifolds, maps between manifolds, and embeddings of manifolds in one another. Included in this sub-branch of Pure Mathematics; knot theory, homotopy, manifold ...
7
votes
2answers
51 views
“tmf(n) is the space of supersymmetric conformal field theories of central charge -n”
I read this intriguing statement in John Baez' week 197 the other day, and I've been giving it some thought. The post in question is from 2003, so I was wondering if there has been any progress in ...
12
votes
2answers
50 views
Numerical Analysis of Elliptic PDEs
I am looking for an elementary reference regarding issues of stability in numerical analysis of non-linear elliptic PDEs, particularly using the finite difference method (but something more ...
7
votes
1answer
78 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 ...
4
votes
1answer
48 views
Spekkens Toy Model, Internal Comonoids
I have been thinking about Spekkens Toy model in terms of interfaces. The Spekkens paper concerns a physics based on only being able to receive answers to half the number of questions necessary to ...
12
votes
2answers
59 views
How much of the Capelli-Itzykson-Zuber ADE-classification of su(2)-conformal field theories can one see perturbatively?
In their celebrated work, Capelli Itzykson and Zuber established an
ADE-classification of modular invariant CFTs with chiral algebra $\mathfrak{su}(2)_k$.
How much of that classification can one ...
5
votes
1answer
61 views
Quantum causal structure
We take causal structure to be some relation defined over elements which are understood to be morphisms of some category. An example of such a relation is a domain, another is a directed acyclic ...
10
votes
2answers
44 views
Examples of heterotic CFTs
I'm trying to get a global idea of the world of conformal field theories.
Many authors restrict attention to CFTs where the algebras of left and right movers agree. I'd like to increase my intuition ...
9
votes
3answers
365 views
Rigorous proof of Bohr-Sommerfeld quantization
Bohr-Sommerfeld quantization provides an approximate recipe for recovering the spectrum of a quantum integrable system. Is there a mathematically rigorous explanation why this recipe works? In ...
9
votes
1answer
322 views
False vacuum in axiomatic QFT
There is an elegant way to define the concept of an unstable particle in axiomatic QFT (let's use the Haag-Kastler axioms for definiteness), namely as complex poles in scattering amplitudes. Stable ...
8
votes
1answer
264 views
Quivers in String Theory
Why do a physicist, particularly a string theorist care about Quivers ?
Essentially what I'm interested to know is the origin of quivers in string theory and why studying quivers is a natural thing ...
14
votes
2answers
123 views
Geometric quantization of identical particles
Background:
It is well known that the quantum mechanics of $n$ identical particles living on $\mathbb{R}^3$ can be obtained from the geometric quantization of the cotangent bundle of the manifold ...
8
votes
0answers
36 views
Minimal strings and topological strings
In http://arxiv.org/abs/hep-th/0206255 Dijkgraaf and Vafa showed that the closed string partition function of the topological B-model on a Calabi-Yau of the form $uv-H(x,y)=0$ coincides with the free ...
8
votes
1answer
256 views
AGT conjecture and WZW model
In 2009 Alday, Gaiotto and Tachikawa conjectured an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov ...
11
votes
2answers
130 views
Literature on fractal properties of quasicrystals
At the seminar where the talk was about quasicrystals, I mentioned that some results on their properties remind the fractals. The person who gave the talk was not too fluent in a rigor mathematics ...
7
votes
1answer
78 views
Characters of $\widehat{\mathfrak{su}}(2)_k$ and WZW coset construction
I am currently studying affine Lie algebras and the WZW coset construction. I have a minor technical problem in calculating the (specialized) character of $\widehat{\mathfrak{su}}(2)_k$ for an affine ...
14
votes
1answer
54 views
Miura transform for W-algebras of exceptional type
Miura transform for W-algebras of classical types can be found in e.g. Sec. 6.3.3 of Bouwknegt-Schoutens. Is there a similar explicit Miura transform for W-algebras of exceptional types, say, E6? It's ...
12
votes
2answers
160 views
Generalized Complex Geometry and Theoretical Physics
I have been wondering about some of the different uses of Generalized Complex Geometry (GCG) in Physics. Without going into mathematical detail (see Gualtieri's thesis for reference), a Generalized ...
8
votes
2answers
136 views
Are there rigorous constructions of the path integral for lattice QFT on an infinite lattice?
Lattice QFT on a finite lattice* is a completely well defined mathematical object. This is because the path integral is an ordinary finite-dimensional integral. However, if the lattice is infinite, ...
15
votes
6answers
201 views
Which QFTs were rigorously constructed?
Which QFTs have mathematically rigorous constructions a la AQFT? I understand there are many such constructions in 2D, in particular 2D CFT has been extensively studied mathematically. But even in 2D ...
5
votes
1answer
25 views
Scaling solutions in context of Denef - Moore
My question is based on the paper Split states, entropy enigma, holes, halos.
What are the scaling solutions discussed on page 49 of the paper ?
It is stated that the equations ${\sum_{j, i\neq ...
8
votes
3answers
48 views
Does the complex 3-sphere have a complex structure modulus?
This question has a flavor which is more mathematical than physical, however it is about a mathematical physics article and I suspect my misunderstanding occurs because the precise mathematical ...
10
votes
3answers
107 views
Physical interpretation to the category of CFTs
This question comes from reading Andre's question where I wandered whether that question even makes sense physically. In mathematics, VOAs form a category, does this category as a whole have a ...
12
votes
2answers
146 views
Topological twists of SUSY gauge theory
Consider $N=4$ super-symmetric gauge theory in 4 dimensions with gauge group $G$. As is explained in the beginning of the paper of Kapustin and Witten on geometric Langlands, this
theory has 3 ...
23
votes
11answers
830 views
Negative probabilities in quantum physics
Negative probabilities are naturally found in the Wigner function (both the original one and its discrete variants), the Klein paradox (where it is an artifact of using a one-particle theory) and the ...
5
votes
1answer
104 views
How Exactly Does Linear Regge Trajectories Imply Stability?
(for a more muddled version, see physics.stackexchange: http://physics.stackexchange.com/questions/14020/whats-with-mandelstams-argument-that-only-linear-regge-trajectories-are-stable)
There is a ...
13
votes
1answer
44 views
Instanton Moduli Space with a Surface Operator
I would like to understand the mathematical language which is relevant to instanton moduli space with a surface operator.
Alday and Tachikawa stated in 1005.4469 that the following moduli spaces are ...
13
votes
5answers
130 views
Other processes than formal power series expansions in quantum field theory calculations
I am not sure if this question is too naive for this site, but here it goes. In QFT calculations, it seems that everything is rooted in formal power series expansions, i.e. , what dynamical systems ...
8
votes
1answer
23 views
Sub and super multiplicativity of norms for understanding non-locality
In relation to various problems in understanding entanglement and non-locality, I have come across the following mathematical problem. It is most concise by far to state in its most mathematical form ...
11
votes
1answer
82 views
Metric interpretation of self-adjoint extensions?
I am wondering if beyond physical interpretation, the one dimensional contact interactions (self-adjoint extensions of the the free Hamiltonian when defined everywhere except at the origin) have a ...
10
votes
2answers
29 views
Extensions of DHR superselection theory to long range forces
For Haag-Kastler nets $M(O)$ of von-Neumann algebras $M$ indexed by open bounded subsets $O$ of the Minkowski space in AQFT (algebraic quantum field theory) the DHR (Doplicher-Haag-Roberts) ...
13
votes
1answer
350 views
Onsager's Regression Hypothesis, Explained and Demonstrated
Onsager's 1931 regression hypothesis asserts that “…the average regression of fluctuations will obey the same laws as the corresponding macroscopic irreversible process". (Here is the links to ...
36
votes
6answers
775 views
The Role of Rigor
The purpose of this question is to ask about the role of mathematical rigor in physics. In order to formulate a question that can be answered, and not just discussed, I divided this large issue into ...
13
votes
3answers
63 views
Status of local gauge invariance in axiomatic quantum field theory
In his recent review...
Sergio Doplicher, The principle of locality: Effectiveness, fate, and challenges, J. Math. Phys. 51, 015218 (2010), doi
...Sergio Doplicher mentions an important open ...
10
votes
0answers
139 views
Hypersingular Boundary Operator in Physics
This has been a question I've been asking myself for quite some time now. Is there a physical Interpretation of the Hypersingular Boundary Operator?
First, let me give some motivation why I think ...
19
votes
2answers
46 views
Bell polytopes with nontrivial symmetries
Take $N$ parties, each of which receives an input $s_i \in {1, \dots, m_i}$ and produces an output $r_i \in {1, \dots, v_i}$, possibly in a nondeterministic manner. We are interested in joint ...
14
votes
4answers
59 views
Why can't noncontextual ontological theories have stronger correlations than commutative theories?
EDIT: I found both answers to my question to be unsatisfactory. But I think this is because the question itself is unsatisfactory, so I reworded it in order to allow a good answer.
One take on ...
