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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 ...
David Bar Moshe's user avatar
69 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 ...
Yuji's user avatar
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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 ...
Alexander Cska's user avatar
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The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations often used in the study of ...
user avatar
53 votes
1 answer
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, ...
xiaohuamao's user avatar
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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-...
André Henriques's user avatar
31 votes
1 answer
701 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 ...
user avatar
29 votes
0 answers
744 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 ...
riemannium's user avatar
  • 6,611
28 votes
1 answer
1k 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 ...
jws's user avatar
  • 401
28 votes
0 answers
523 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 ...
user avatar
27 votes
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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 ...
Urs Schreiber's user avatar
24 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 ...
user110373's user avatar
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24 votes
0 answers
512 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 ...
Urs Schreiber's user avatar
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 ...
Sebastien Palcoux's user avatar
22 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 ...
Mike's user avatar
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22 votes
0 answers
622 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 ...
Michael's user avatar
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20 votes
1 answer
492 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(...
tparker's user avatar
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20 votes
1 answer
549 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 ...
ACuriousMind's user avatar
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20 votes
0 answers
887 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. ...
wonderich's user avatar
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18 votes
1 answer
2k views

How to show the Gauss-Bonnet term is a total derivative?

It is well-known that the Gauss-Bonnet term $$\mathcal L_G =R^2 -4 R_{\mu\nu}R^{\mu\nu}+R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}\tag 1$$ does not contribute to the equations of motion when adding it ...
user avatar
18 votes
1 answer
747 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 ...
DanielSank's user avatar
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18 votes
0 answers
538 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 ...
Ryan Thorngren's user avatar
17 votes
1 answer
505 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 ...
Martino's user avatar
  • 3,279
17 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} ...
wonderich's user avatar
  • 7,848
17 votes
2 answers
774 views

Is the helium atom with only a contact interaction between the electrons solvable?

Consider the hamiltonian for a helium atom, $$ H=\frac12\mathbf p_1^2+\frac12\mathbf p_2^2 - \frac{2}{r_1}-\frac{2}{r_2} + a \, \delta(\mathbf r_1-\mathbf r_2), $$ where I have taken out the ...
Emilio Pisanty's user avatar
16 votes
0 answers
254 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 ...
Andi Bauer's user avatar
16 votes
0 answers
271 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 ...
OrangeCalx01's user avatar
16 votes
0 answers
617 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 ...
user avatar
15 votes
0 answers
235 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 ...
spiridon_the_sun_rotator's user avatar
15 votes
2 answers
729 views

Is zitterbewegung physical or not?

It appears that zitterbewegung, a frequency associated with the total energy of a particle or system, is widely considered to be an unphysical quantity (e.g., Kobakhidze et.al.), @Lubos Motl, McMillan)...
S. McGrew's user avatar
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15 votes
2 answers
511 views

Regularization: What is so special about the Coulomb/Newtonian and harmonic potential?

I wanted to know if the procedure for regularization of the Coulomb potential outlined in Celletti (2003): Basics of regularization theory could be generalized to arbitrary polynomial potentials. So ...
asmaier's user avatar
  • 9,890
15 votes
0 answers
871 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 ...
mavzolej's user avatar
  • 2,921
15 votes
0 answers
270 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 ...
Anonymous's user avatar
  • 301
15 votes
1 answer
984 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 ...
Sidhha's user avatar
  • 259
15 votes
0 answers
276 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 $$ W= \frac12 h_1 X\Phi_1^2 +\frac12 h_2 \Phi_2\Phi_1^2 + fX.$$ ...
jj_p's user avatar
  • 1,204
15 votes
1 answer
349 views

What is the full algebra of BRST-invariant observables for general relativity?

The Hamiltonian formulation of general relativity - either in the ADM formalism or in Ashtekar variables - is straightforwardly a gauge theory. While the BRST formalism has primarily been developed to ...
ACuriousMind's user avatar
  • 126k
14 votes
0 answers
436 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)\...
Wein Eld's user avatar
  • 3,691
14 votes
0 answers
335 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 ...
user929304's user avatar
  • 4,675
14 votes
0 answers
311 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 ...
Danu's user avatar
  • 16.4k
14 votes
0 answers
377 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?
Hamurabi's user avatar
  • 1,323
14 votes
4 answers
977 views

Molecular origin of solid-liquid and solid-vapour surface tension

I understand that surface tension arises at the liquid-vapour interface due to the asymmetric nature of long-range attractive forces and the short-range repulsive forces acting on the interface where ...
Apoorv Potnis's user avatar
13 votes
0 answers
185 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 ...
Davius's user avatar
  • 1,640
13 votes
0 answers
380 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 ...
ohwilleke's user avatar
  • 3,957
13 votes
1 answer
2k views

The role of the virtual work principle

Lanczos' masterpiece "The Variational Principle of Mechanics" has, on page 76, the following statement: Postulate A (virtual work): The virtual work of the forces of reaction is always zero for any ...
QuantumBrick's user avatar
  • 4,043
13 votes
1 answer
732 views

Trying to solve 2D Toda Lattice Equation with Lax Pair Approach

I am working on this Hamiltonian: $$ H = \frac{p_1^2 + p_2^2}{2m} + e^{q_2-q_1} + e^{q_2} + e^{-q_1} -3 $$ Thank you for the hint that it is a modification of the Toda Lattice Equation. Let me sketch ...
varantir's user avatar
  • 293
13 votes
0 answers
262 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 ...
Emilio Pisanty's user avatar
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 ...
FrancisFlute's user avatar
  • 1,106
13 votes
1 answer
807 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 ...
bolbteppa's user avatar
  • 4,101
13 votes
1 answer
527 views

Why is it hard to give a lattice definition of string theory?

In Polyakov's book, he explains that one possible way to compute the propagator for a point particle is to compute the lattice sum $\sum_{P_{x,x'}}\exp(-m_0L[P_{x,x'}])$, where the sum goes over all ...
Matthew's user avatar
  • 1,800
12 votes
0 answers
383 views

Deriving non-relativistic potentials from QFT

Some systems, like atoms, are described well by quantum mechanics, where one just gives the Hamiltonian in the form $H=T+V$ and computes the eigenvalues and eigenvectors of this operator to figure out ...
OutrageousKangaroo's user avatar

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