All Questions
46,065
questions with no upvoted or accepted answers
90
votes
0
answers
4k
views
Orbits of maximally entangled mixed states
It is well known (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 each stratum corresponds ...
- 30.1k
67
votes
1
answer
4k
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 ...
- 3,582
63
votes
0
answers
4k
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 ...
- 1,199
57
votes
0
answers
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The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations often used in the study of ...
Zoran Škoda
52
votes
0
answers
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, ...
- 3,562
46
votes
0
answers
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 a simple toy model with lagrangian (from Wikipedia)
$
\mathcal{...
- 825
41
votes
0
answers
1k
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-...
- 531
34
votes
1
answer
588
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 signatures that ...
- 576
31
votes
0
answers
606
views
Minimal strings and topological strings
In this study 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 energy of a certain ...
Pavel Safronov
28
votes
0
answers
701
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. On the other hand, the ...
- 6,327
28
votes
0
answers
475
views
Quantum statistics of branes
Quantum statistics of particles (bosons, fermions, anyons) arise due to the possible topologies of curves in $D$-dimensional spacetime winding around each other
What happens if we replace particles ...
Squark
27
votes
1
answer
886
views
Electric charges on compact four-manifolds
Textbook wisdom in electromagnetism tells you that there is no total electric charge on a compact manifold. For example, consider space-time of the form $\mathbb{R} \times M_3$ where the first factor ...
- 391
25
votes
0
answers
1k
views
$p$-Adic String Theory and the String-orientation of Topological Modular Forms (tmf)
I am going to ask a question, at the end below, on whether anyone has tried to make more explicit what should be a close relation between p-adic string theory and the refinement of the superstring ...
- 13.5k
24
votes
0
answers
468
views
Super Lie-infinity algebra of closed superstring field theory?
Bosonic closed string field theory is famously governed by a Lie n-algebra for $n = \infty$ whose $k$-ary bracket is given by the genus-0 (k+1)-point function in the BRST complex of the string.
One ...
- 13.5k
23
votes
0
answers
1k
views
TQFTs and Feynman motives
Questions
Is a topological quantum field theory metrizable? Or else a TQFT coming from a subfactor?
For a given metric, are there always renormalization and Feynman diagrams?
Is there always a Feynman ...
22
votes
0
answers
487
views
Definition of vacua in QFT in generic spacetimes
I have been learning QFT in curved spaces from various sources (Birrell/Davies, Tom/Parker, some papers), and one thing that confuses me the most is the choice of vacua in various spacetimes, and the ...
- 1,598
22
votes
0
answers
599
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 ...
- 1,223
21
votes
0
answers
584
views
Phil Anderson's Criticism of Existence of Stable Dissipative Structures
In this book chapter (1987), titled "Broken symmetry, emergent properties, dissipative structures, life," Phil Anderson and Daniel Stein criticize defining life as a dissipative structure (a ...
- 582
21
votes
0
answers
4k
views
Where does the Berry phase of $\pi$ come from in a topological insulator?
The Berry connection and the Berry phase should be related. Now for a topological insulator (TI) (or to be more precise, for a quantum spin hall state, but I think the Chern parities are calculated in ...
- 672
20
votes
0
answers
469
views
Why is full M-theory needed for compactification on singular 7-folds and what does that even mean?
In "M-theory on manifolds of $G_2$ holonomy: the first twenty years" by Duff, it is claimed (e.g. in section 8) that for compactification on singular 7-folds to be possible, we need to consider not ...
- 120k
20
votes
0
answers
1k
views
Why does analytic continuation as a regularization work at all?
The question is about why analytical continuation as a regularization scheme works at all, and whether there are some physical justifications. However, as this is a relatively general question, I ...
- 1,319
20
votes
0
answers
858
views
Orbifold CFT of $SU(2)/G$ and $SO(3)/G$
In this paper by Dijkgraaf, Vafa, Verlinde, Verlinde, orbifold CFT is discussed.
In that paper, it outlined that orbifold CFT provides a way to generate the new theories from the old known ones. (i.e. ...
- 7,670
18
votes
0
answers
520
views
Compactifying on a circle and the exchange of R and NS sectors
I've noticed a general phenomenon in compactifying on a circle where if you start with, say, an NS field, then the KK fields with an index along the circle will be in the R sector, and those without ...
- 7,853
17
votes
1
answer
457
views
Renormalisation and the Fisher-Rao metric
The renormalisation group (I'm talking about classical, statistical physics here, I'm not familiar with field theory too much) can be thought of as a flux in a space of possible Hamiltonians for a ...
- 3,243
16
votes
0
answers
298
views
What are the exact relations between bound states, discrete spectra, and negative energies in quantum mechanics?
Consider the nonrelativistic quantum mechanics of one particle in one dimension ("NRQMOPOD") with the time-independent Schrodinger equation
$$
\left( -\frac{\hbar^2}{2m} \frac{d^2}{dx^2} + V(...
- 46.2k
16
votes
1
answer
613
views
How does one compute the state of a quantum system following imperfect measurement?
Suppose I have a quantum system $S$ ("system") with Hamiltonian $H_S$ and initial density matrix $\rho_S(0)$.
I allow $S$ to interact with another system $P$ ("probe"), which has Hamiltonian $H_P$ and ...
- 24.1k
16
votes
0
answers
253
views
Why do flux qubits have to be micrometer-sized?
Flux qubits are made using micrometer sized Josephson junctions. They exploit superconducting properties to create and interfere with the magnetic flux between them.
My question is that I've seen ...
- 261
16
votes
0
answers
1k
views
Time Reversal, CPT, spin-statistics, mass gap and chirality of Euclidean fermion field theory
In Minkowski space even-dim (say $d+1$ D) spacetime dimension, we can write fermion-field theory as the Lagrangian:
$$
\mathcal{L}=\bar{\psi} (i\not \partial-m)\psi+ \bar{\psi} \phi_1 \psi+\bar{\psi} ...
- 7,670
16
votes
0
answers
588
views
Measure of Lee-Yang zeros
Consider a statistical mechanical system (say the 1D Ising model) on a finite lattice of size $N$, and call the corresponding partition function (as a function of, say, real temperature and real ...
user3657
15
votes
0
answers
227
views
About variational methods, renormalization and $a$, $c$-theorems
Variational approximation
Variational methods are an important technique, frequently applied for the approximation of complicated probability distributions, with the applications in statistical ...
- 4,782
15
votes
0
answers
781
views
Wick theorem and OPE
I'm trying to work out in detail how the Wick theorem is used for constructing OPEs in CFT. One of the first things which bothers me is the difference in definitions of normal ordered product and ...
- 2,684
15
votes
0
answers
2k
views
How to show the Gauss-Bonnet term is a total derivative?
It is well-known that the Gauss-Bonnet term
$$\mathcal L_G =R^2 -4 R_{\mu\nu}R^{\mu\nu}+R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}\tag 1$$
do not contribute to equations of motion when adding it to the ...
user146681
15
votes
0
answers
247
views
Is it known what the necessary and sufficient conditions are for the existence of a "3+1 split" (by means of a foliation) of a (Lorentzian) manifold?
When trying to do physics on a more general pseudo-Riemannian manifold we want to require that there is a foliation of this manifold into three-dimensional subspaces. By this I mean we would like to ...
- 301
15
votes
3
answers
293
views
To what extent can one recover plane waves from the Airy eigenfunctions of a linear potential as the field is turned off?
Consider a single massive particle in one dimension under the action of a static linear potential, with the hamiltonian
$$
\hat H=\frac{\hat p^2}{2}+\hat{x}F_0.
$$
The eigenstate at energy $E$ is, ...
- 129k
15
votes
0
answers
2k
views
What is "spin-orbit torque?"
I am trying really hard to understand the concept of spin-orbit torque. It is a new-ish discovery in the field of spintronics and has many applications for magnetic devices. The information that has ...
- 469
15
votes
1
answer
934
views
Kolmogorov/Energy spectrum for turbulent boundary layer
Previously, I have calculated energy spectrum for 3D isotropic turbulent flow data which is equally spaced in all three directions and then to compute the energy spectrum, one performs Fourier ...
- 259
15
votes
2
answers
548
views
Is there an analogue of the LSZ reduction formula in quantum mechanics?
In quantum field theory the LSZ reduction formula gives us a method of calculating S-matrix elements. In order to understand better scattering in QFT, I will study scattering in non-relativistic ...
- 1,015
14
votes
0
answers
593
views
Radiative corrections to Coulomb’s law and Euler-Heisenberg theory
Maxwell's electrodynamics is the classical limit of QED (quantum electrodynamics). Using Maxwell's equations, the electrostatic (Coulomb) potential of a point charge is obtained as $\Phi \propto \frac{...
- 4,530
14
votes
0
answers
393
views
How to perform a derivative of a functional determinant?
Let us consider a functional determinant
$$\det G^{-1}(x,y;g_{\mu\nu})$$
where the operator $G^{-1}(x,y;g_{\mu\nu})$ reads
$$G^{-1}(x,y;g_{\mu\nu})=\delta^{(4)}(x-y)\sqrt{-g(y)}\left(g^{\mu\nu}(y)\...
- 3,573
14
votes
0
answers
187
views
Do correlations in local quantum spin systems always decay exponentially or algebraically?
Consider translation-invariant quantum spin systems, that is qu-d-its on a lattice with a geometrically local Hamiltonian. Usually, such models are either gapped (in an ordered/disordered phase) or ...
- 301
14
votes
0
answers
318
views
Demystifying jamming in many-body systems
From a theoretical point of view, what has been the most successful approach to understanding jamming phenomena?
I understand there's still a lot of debate around this subject, namely whether a ...
- 4,485
14
votes
0
answers
302
views
What is the stringy interpretation of the cohomology classes arising from the Kähler class?
In superstring theory, one usually considers compactifications on Calabi-Yau 3-manifolds. These manifolds are in particular compact Kähler, hence possess a Kähler class which gives rise to nontrivial ...
- 16.2k
14
votes
0
answers
266
views
Simple argument for unexpected behavior in SUSY model
Consider a supersymmetric theory with 3 chiral superfields, $X, \Phi_1$ and $\Phi_2,$ with canonical Kahler potential and superpotential
$$ W= \frac12 h_1 X\Phi_1^2 +\frac12 h_2 \Phi_2\Phi_1^2 + fX.$$
...
- 1,134
14
votes
0
answers
363
views
Topological entanglement entropy only defined for a system in the ground state?
What happens to the topological entanglement entropy of a system, when it is driven out of its groundstate by increasing the temperature?
- 1,303
13
votes
0
answers
158
views
Is it known whether Wightman's axiomatic QFT is logically equivalent to Osterwalder–Schrader's axiomatic QFT?
Constructive QFT has provided some interesting models for dimension $d < 4$ of space-time, satisfying specific axiomatic versions of QFT. On the other hand, it is a well known fact that an ...
- 1,433
13
votes
0
answers
319
views
Are there any experimental bounds on the ratio of neutrinos to antineutrinos in the universe?
In the Standard Model, both baryon number and lepton number are conserved quantities (excluding the theoretical possibility of sphaleron processes which are exceeding rare, at least at non-"near in ...
- 3,873
13
votes
1
answer
1k
views
Sequential Stern-Gerlach devices - realizable experiment or teaching aid?
At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
- 14.6k
13
votes
0
answers
247
views
A beautiful ion-trap proposal for Boson Sampling: what are its limitations?
A very beautiful recent paper,
Scalable Implementation of Boson Sampling with Trapped Ions. C. Shen, Z. Zhang, and L.-M. Duan. Phys. Rev. Lett. 112 no. 5, 050504 (2014); arXiv:1310.4860
describes ...
- 129k
13
votes
0
answers
1k
views
Penrose's Zig-Zag Model and Conservation of Momentum
I was reading through Penrose's Road to Reality when I saw his interesting description of the Dirac electron (Chapter 25, Section 2). He points out that in the two-spinor formalism, Dirac's one ...
- 1,076
13
votes
1
answer
743
views
Interpreting the Klein-Gordon Annihilation Operator Expression
I can derive $$a(k) = \int d^3 x e^{ik_{\mu} x^{\mu}} (\omega_{\vec{k}} \psi + i \pi)$$ for a free real scalar Klein-Gordon field in three ways mathematically: the usual Fourier transform way in ...
- 3,866