Unanswered Questions
37,923 questions with no upvoted or accepted answers
123
votes
0answers
6k views
Linear sigma models and integrable systems
I'm a mathematician who recently became very interested in questions related to mathematical physics but somehow, I faced difficulties in penetrating the literature... I'd highly appreciate any help ...
107
votes
0answers
5k views
Experimental test of the non-statisticality theorem?
Context: The paper On the reality of the quantum state (Nature Physics 8, 475–478 (2012) or arXiv:1111.3328) shows under suitable assumptions that the quantum state cannot be interpreted as a ...
81
votes
0answers
3k views
Orbits of maximally entangled mixed states
It is well known (Please, see for example Geometry of quantum states by Bengtsson and Życzkowski ) that the set of $N$-dimensional density matrices is stratified by the adjoint action of $U(N)$, where ...
65
votes
1answer
3k views
On the Coulomb branch of ${\cal N}=2$ supersymmetric gauge theory
The chiral ring of the Coulomb branch of a 4D ${\cal N}=2$ supersymmetric gauge theory is given by the Casimirs of the vector multiplet scalars, and they don't have non-trivial relations; the Casimirs ...
55
votes
0answers
1k views
Systematic approach to deriving equations of collective field theory to any order
The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...
46
votes
0answers
2k views
How to apply the Faddeev-Popov method to a simple integral
Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
46
votes
0answers
2k views
Can Lee-Yang zeros theorem account for triple point phase transition?
Now the prominent Lee-Yang theorem (or Physical Review 87, 410, 1952) has almost become a standard ingredient of any comprehensive statistical mechanics textbook.
If the volume tends to infinity, ...
41
votes
0answers
2k views
$\operatorname{O}(N)$ sigma model at large $N$
I would like to better understand the main principles of large-$N$ expansion in quantum field theory. To this end I decided to consider simple toy-model with lagrangian (from Wikipedia)
$
\mathcal{L} ...
40
votes
0answers
941 views
Positivity for the level of Chern-Simons theory
In many classical papers about Chern-Simons theory (see, e.g. [1]),
it is claimed that the Chern-Simons theories with gauge group $G$ are classified by an element of $k\in H^4(BG,\mathbb Z)$, the so-...
30
votes
1answer
1k views
What is the largest number of bosons placed in a BEC?
What is the record for the largest number of bosons placed in a Bose-Einstein condensate?
What are the prospects for how high this might get in the future?
EDIT: These guys reported 20 million ...
29
votes
0answers
479 views
Is there any way to distinguish experimentally gauge mediation from gravity mediation in an unambiguous way?
There are lots of models of gravity mediated SUSY breaking with various spectra as well as various general gauge mediation models. Are there any "smoking gun" experimental singnatures that could ...
27
votes
0answers
446 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 ...
25
votes
1answer
329 views
Is the converse of Weinberg's statement on the cluster decomposition principle true?
In Weinberg's "The Quantum Theory of Fields, Vol. 1", Section 4.4, page 182, the author says:
We now ask, what sort of Hamiltonian will yield an $S$-matrix that satisfies the cluster ...
25
votes
0answers
552 views
Extended Born relativity, Nambu 3-form and ternary ($n$-ary) symmetry
Background: Classical Mechanics is based on the Poincare-Cartan two-form
$$\omega_2=dx\wedge dp$$
where $p=\dot{x}$. Quantum mechanics is secretly a subtle modification of this. By the other hand, the ...
25
votes
0answers
324 views
Quantum statistics of branes
Quantum statistics of particles (bosons, fermions, anyons) arises due to the possible topologies of curves in $D$-dimensional spacetime winding around each other
What happens if we replace particles ...
