The research-level tag applies to questions that arise in graduate and post-secondary work. These questions often require domain-specific knowledge and could not be answered from a general source or may be beyond the level typically covered by Wikipedia and other popular sources. research-level ...
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117 views
Relevance of SIC-POVMs to quantum information
What is the real relevance of SIC-POVMs (symmetric informationally complete POVMs) to concrete tasks in quantum information theory? A lot of work has been put into giving explicit constructions, and ...
15
votes
1answer
131 views
Models of higher Chern-Simons type
It has long been clear that (the action functional of) Chern-Simons theory has various higher analogs and variations of interest. This includes of course traditional higher dimensional Chern-Simons ...
15
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0answers
105 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The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...
14
votes
6answers
308 views
Classic Literature in Quantum Gravity?
I've seen it said in various places that a major reason people like string theory as a theory of quantum gravity is that it does a good job of matching our prejudices about how a quantum gravity ...
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 ...
14
votes
3answers
206 views
Which exact solutions of the classical Yang-Mills equations are known?
I'm interested in the pure gauge (no matter fields) case on Minkowski spacetime with simple gauge groups.
It would be nice if someone can find a review article discussing all such solutions
EDIT: I ...
14
votes
1answer
186 views
Why isn't the Gear predictor-corrector algorithm for integration of the equations of motion symplectic?
Okumura et al., J. Chem. Phys. 2007 states that the Gear predictor-corrector integration scheme, used in particular in some molecular dynamics packages for the dynamics of rigid bodies using ...
14
votes
1answer
167 views
Is string theory local?
By locality I mean something like the Atiyah-Segal axioms for Riemannian cobordisms (see e.g. http://ncatlab.org/nlab/show/FQFT). I.e. to any (spacelike) hypersurface in the target we associate a ...
14
votes
6answers
105 views
Multiqubit state tomography by performing measurement in the same basis
For a $n$-qubit state $\rho$ we perform all projective measurement consisting of one-particle measurements in the same basis, that is,
$$p_{i_1i_2\ldots i_n}(\theta,\varphi) = \text{Tr}\left \{ \rho ...
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 ...
14
votes
1answer
109 views
Do Gauge Theories (CFTs) Have Phase Transitions as the 't Hooft Coupling is Varied?
With an eye toward AdS/CFT, I'm wondering if large $N$ CFTs have a (quantum) phase transition as the 't Hooft coupling is varied. To be more specific -- if I look at correlation functions of ...
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 ...
14
votes
2answers
51 views
Counting complete sets of mutually unbiased bases composed of stabilizer states
Consider $N$ qubits. There are many complete sets of $2^N+1$ mutually unbiased bases formed exclusively of stabilizer states. How many?
Each complete set can be constructed as follows: partition the ...
14
votes
0answers
174 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 ...
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 ...
13
votes
6answers
252 views
Is there a theorem that says that QFT reduces to QM in a suitable limit? A theorem similar to Ehrenfest's theorem?
Is there a theorem that says that QFT reduces to QM in a suitable limit?
Of course, it should be, as QFT is relativisitc quantum mechanics.
But, is there a more manifest one? such as Ehrenfest's ...
13
votes
3answers
64 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 ...
13
votes
2answers
65 views
Calculating correlation functions of exponentials of fields
In their book Condensed Matter Field Theory, Altland and Simons often use the following formula for calculating thermal expectation values of exponentials of a real field $\theta$:
$$ \langle ...
13
votes
2answers
127 views
Which CFTs have AdS/CFT duals?
The AdS/CFT correspondence states that string theory in an asymptotically anti-De Sitter spacetime can be exactly described as a CFT on the boundary of this spacetime.
Is the converse true? Does any ...
13
votes
2answers
158 views
Applications of the Feynman-Vernon Influence Functional
I am looking for a reference where the Feynman-Vernon influence functional was defined and used in the context of relativistic quantum field theory. This functional is one method to describe ...
13
votes
1answer
181 views
Sympletic structure of General Relativity
Inspired by physics.SE: http://physics.stackexchange.com/questions/15571/does-the-dimensionality-of-phase-space-go-up-as-the-universe-expands/15613
It made me wonder about symplectic structures in ...
13
votes
1answer
94 views
realization of: CFT generating fuction = AdS partition function
An important aspect of the AdS/CFT correspondence is the recipe to compute correlation functions of a boundary operator $\mathcal{O} $ in terms of the supergravity fields in the interior of the ...
13
votes
2answers
437 views
Topological Charge. What is it Physically?
I have seen the term topological charge defined in an abstract mathematical way as a essentially a labeling scheme for particles which follows certain rules. However I am left guessing when trying to ...
13
votes
2answers
158 views
A resource theory of quantum discord?
Local Operations and Classical Communication (LOCC) is the classic paradigm for studying entanglement. These are things that are `cheap' and unable to produce entanglement as a resource for a quantum ...
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 ...
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
1answer
109 views
Monte Carlo integration over space of quantum states
I am currently facing the problem of calculating integrals that take the general form
$\int_{R} P(\sigma)d\sigma$
where $P(\sigma)$ is a probability density over the space of mixed quantum states, ...
13
votes
2answers
64 views
Uniqueness of supersymmetric heterotic string theory
Usually we say there are two types of heterotic strings, namely $E_8\times E_8$ and $Spin(32)/\mathbb{Z}_2$. (Let's forget about non-supersymmetric heterotic strings for now.)
The standard argument ...
13
votes
2answers
395 views
What does the sum of two qubits tell about their correlations?
How much can I learn about correlations between two quits by measuring
the sum of their values? What is the best way to formalize such a
question?
Below is my original, longer formulation of ...
13
votes
1answer
72 views
Phase Transition in the Ising Model with Non-Uniform Magnetic Field
Consider the Ferromagnetic Ising Model ($J>0$) on the lattice $\mathbb{Z}^2$ with the Hamiltonian with boundary condition $\omega\in\{-1,1\}$ formally given by
$$
...
13
votes
2answers
29 views
Sampling typical clusters between distant points in subcritical percolation
I have on several occasions wondered how one might proceed in order to sample large subcritical Bernoulli bond-percolation clusters, say on the square lattice.
More precisely, let's consider the ...
13
votes
1answer
31 views
SuperHiggs Mechanism on different Backgrounds & Compactifications
I've been studying Bagger & Giannakis paper on the SuperHiggs Mechanism found here.
The paper shows how SUSY is broken by a $B_{\mu\nu}$ gauge field background restricted to $T^3$ in $M^7\times ...
12
votes
4answers
208 views
direct sum of anyons?
In the topological phase of a fractional quantum Hall fluid, the excitations of the ground state (quasiparticles) are anyons, at least conjecturally.
There is then supposed to be a braided fusion ...
12
votes
4answers
2k views
A pedestrian explanation of conformal blocks
I would be very happy if someone could take a stab at conveying what conformal blocks are and how they are used in conformal field theory (CFT). I'm finally getting the glimmerings of understanding ...
12
votes
5answers
303 views
Does Kaluza-Klein theory successfully unify GR and EM? Why can't it be extended to the Standard Model gauge group?
As a quick disclaimer, I thought this might be a better place to ask than Physics.SE. I already searched there with "kaluza" and "klein" keywords to find an answer, but without luck. As background, ...
12
votes
4answers
450 views
Tree level QFT and classical fields/particles
It is well known that scattering cross-sections computed at tree level correspond to cross-sections in the classical theory. For example the tree level cross-section for electron-electron scaterring ...
12
votes
2answers
181 views
Renormalization in string theory
I'm taking a course in string theory and have encountered renormalization for the first time (and I suspect it isn't the last).
Specifically, while quantizing the bosonic and spinning strings, an ...
12
votes
2answers
162 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 ...
12
votes
2answers
148 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 ...
12
votes
2answers
91 views
Random Walk Randomly Reflected
Hi I am not specialist in probability so I will not be surprised if the answer for this question is just a simple consequence of well known results from the random walk theory.
In this case, I will ...
12
votes
1answer
82 views
What is the Holevo-Schumacher-Westmoreland capacity of a Pauli channel?
Suppose you are given an $n$-qubit quantum channel defined as $\mathcal{E}(\rho) = \sum_{i} p_i X_i \rho X_i^\dagger$, where $X_i$ denotes an $n$-fold tensor product of Pauli matrices and $\{p_i\}$ is ...
12
votes
1answer
55 views
Explicit construction for unitary extensions of CPTP maps?
Given a completely positive and trace preserving map $\Phi : \textrm{L}(\mathcal{H})\to\textrm{L}(\mathcal{G})$, it is clear by the Kraus representation theorem that there exist $A_k \in ...
12
votes
1answer
154 views
What is a “free” non-Abelian Yang-Mill's theory?
I hope this question will not be closed down as something completely trivial!
I did not think about this question till in recent past I came across papers which seemed to write down pretty much ...
12
votes
2answers
68 views
Decoherence and measurement in NMR
It seems that the Bloch equations, or a suitable generalization thereof, are enough to phenomenologically model the measurement process in NMR. Has anyone attempted a fully quantum mechanical model ...
12
votes
2answers
1k views
What is a resonating valence bond (RVB) state?
There's something known as a "resonating valence bond" (RVB) state, which plays a role in at least some attempts to understand physics of high-$T_c$ superconductors. This, roughly, involves a state ...
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 ...
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 ...
12
votes
1answer
50 views
Local Fermionic Symmetry
That is perhaps a bit of an advertisement, but a couple of collaborators and myself just sent out a paper, and one of the results there is a little bit surprising. We found (in section 6E) a fermionic ...
12
votes
1answer
93 views
6d Massive Gravity
Massive gravity (with a Fierz-Pauli mass) in 4 dimensions is very well-studied, involving exotic phenomena like the vDVZ discontinuity and the Vainshtein effect that all have an elegant and physically ...
11
votes
3answers
973 views
How Non-abelian anyons arise in solid-state systems?
Recently it has been studied non-abelian anyons in some solid-state systems. These states are being studied for the creation and manipulation of qubits in quantum computing.
But, how these ...
