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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0answers
167 views
Quasi 1D insulators with strong spin-orbital interaction
We know that the spin-1 chain realizes the Haldane phase which is an example of
symmetry protected topological (SPT) phases (ie short-range entangled phases with symmetry). The Haldane phase is ...
7
votes
2answers
445 views
Majorana zero mode in quantum field theory
Recently, Majorana zero mode becomes very hot in condensed matter physics.
I remember there was a lot of study of fermion zero mode
in quantum field theory, where advanced math, such as index ...
17
votes
10answers
1k views
What is spontaneous symmetry breaking in QUANTUM systems?
Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture.
According to the classical picture, spontaneous ...
3
votes
1answer
119 views
How can you distinguish between projections of quantum states?
Consider this problem in quantum cryptography:
We have two pure states $\phi_1,\phi_2$ as input and constants $0 \leq \alpha <\beta \leq 1 $, where "Yes instances" are those for which ...
5
votes
1answer
176 views
The bijective correspondence between a symmetric polynomial and edge excitation of the fractional quantum hall droplet
I am recently reading Xiao-Gang Wen's paper (http://dao.mit.edu/~wen/pub/edgere.pdf) on edge excitation for fractional quantum hall effect. On page 25, he claimed that it is easy to show that there ...
4
votes
2answers
280 views
What causes a Phase-Transition
A phase transition occurs when for example, heat is applied continuously to a liquid and after a certain time it converts into a gas.
How does this process work in detail? Is their a chain reaction ...
4
votes
1answer
585 views
What is the relationship between string net theory and string / M-theory?
I've just learned from this one of Prof. Wen's answers that there exists a theory called string net theory. Since I've never heard about this before it picks my curiosity, so I`d like to ask some ...
9
votes
3answers
437 views
Is there any quantum-gravity theory that has flat space-time and gravitons?
Many quantum-gravity theories are strongly interacting. It is not clear
if they produce the gravity as we know it at low energies. So I wonder, is there
any quantum-gravity theory that
a) is a well ...
5
votes
1answer
269 views
Graphene Moebius Strip
I'm refering to the Paper:
PHYSICAL REVIEW B 80, 195310 (2009)
"Möbius graphene strip as a topological insulator"
Z. L. Guo, Z. R. Gong, H. Dong, and C. P. Sun.
The paper is also available as a ...
3
votes
0answers
135 views
Toda equations and surface operator
I would like to know the reason why the equation (14) in the paper by Yamada is called the Toda equation.
\begin{equation}
\left[\frac12\sum_{i=1}^N\left(y_i\frac{\partial}{\partial ...
5
votes
2answers
196 views
Branch-point twist fields and operator insertions on a Riemann manifold
I am having trouble understanding how Eq (2.6) in this paper (PDF)
$$Z[\mathcal{L},\mathcal{M}_{n}]\propto\langle\Phi(u,0)\tilde{\Phi}(v,0)\rangle_{\mathcal{L}^{(n)},\mathbb{R}^{2}}$$
generalizes to ...
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 ...
5
votes
2answers
189 views
Poincare Symmetry in QFT
Given that spacetime is not affine Minkowskispace, it does of course not possess Poincare symmetry. It is still sensible to speak of rotations and translations (parallel transport), but instead of
...
7
votes
0answers
109 views
What is a Hilbert space filter?
In a recent paper,
Side-Channel-Free Quantum Key Distribution, by Samuel L. Braunstein and Stefano Pirandola. Phys. Rev. Lett. 108, 130502 (2012). doi:10.1103/PhysRevLett.108.130502, ...
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
...
6
votes
1answer
158 views
partial trace with sparse matrices
Let $\rho_{ABCD}$ be a sparse matrix of 4 systems each in a $d$-dimensional Hilbert space.
For $d<7$ in a reasonable time (few seconds) I able to perform the partial trace $\rho_{AD}$ using the ...
3
votes
3answers
88 views
QED as a Wightman theory of observable fields? With a collision theory?
[Note: I'm using QED as a simple example, despite having heard that it
is unlikely to exist. I'm happy to confine the question to
perturbation theory.]
The quantized Aᵘ and ψ fields are non-unique ...
5
votes
3answers
99 views
What is the physical difference between states and unital completely positive maps?
Mathematically, completely positive maps on C*-algebras generalize positive linear functionals in that every positive linear functional on a C*-algebra $A$ is a completely positive map of $A$ into ...
2
votes
0answers
55 views
Why/When can the gauge superfield and/or chiral superfield kinetic term in $(2,2)$ SUSY be ignored?
This is in reference to the argument given towards the end of page $61$ of this review paper. There for the path-integral argument to work the author clearly needed some argument to be able to ignore ...
7
votes
2answers
117 views
Could motives aid in the study of the Navier-Stokes equations?
Recently, mathematicians and theoretical physicists have been studying Quantum Field Theory (and renormalization in particular) by means of abstract geometrical objects called motives. Amongst these ...
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 ...
6
votes
1answer
257 views
About the definition/motivation/properties of the twisted chiral superfield in ${\cal N}=2$ theories in $1+1$ dimensions
The following is in the context of the ${\cal N}=2$ supersymmetry in $1+1$ dimensions - which is probably generically constructed as a reduction from the ${\cal N}=1$ case in $3+1$ dimensions.
In ...
4
votes
0answers
97 views
From vertex function to anomalous dimension
In a $d$ dimensional space-time, how does one argue that the mass dimension of the $n-$point vertex function is $D = d + n(1-\frac{d}{2})$?
Why is the following equality assumed or does one prove ...
6
votes
1answer
49 views
States diagonal in the tensor product of Bell states.
Bell-diagonal states are 2-qubit states that are diagonal in the Bell basis. Since those states lie in $\mathbb{C}^{2} \otimes \mathbb{C}^{2}$, the Peres-Horodecki criterion is a sufficient condition ...
6
votes
1answer
68 views
Asymptotic Completeness, generalized free fields, and the relationship of thermodynamics with infinity
Asymptotic completeness is a strong constraint on quantum field theories that rules out generalized free fields, which otherwise satisfy the Wightman axioms. If we were to take a limit of a list of ...
5
votes
2answers
56 views
Heuristics for definitions of open and closed quantum dynamics
I've been reading some of the literature on "open quantum systems" and it looks like the following physical interpretations are made:
Reversible dynamics of a closed quantum system are represented ...
2
votes
1answer
22 views
Time Evolution of a Manifold Embedding
Given a smooth manifold $\mathcal{M}$ with a simplicial complex embedding $\mathsf{S}$, what specific tools or methods can be used to give an analysis of the time evolution of the manifold given some ...
5
votes
1answer
29 views
Gravitating sigma models
I am looking for a review or book on sigma models in (super)gravity theories, which arise from dimensional reduction.
4
votes
1answer
74 views
$\pm$ (light-cone?) notation in supersymmetry
I would like to know what is exactly meant when one writes $\theta^{\pm}, \bar{\theta}^\pm, Q_{\pm},\bar{Q}_{\pm},D_{\pm},\bar{D}_{\pm}$.
{..I typically encounter this notation in literature on ...
3
votes
1answer
39 views
Spectrum of Free Strings
As far as I understand, both in bosonic and superstring theory one considers initially a free string propagating through D-dimensional Minkowskispace. Regardless of what quantization one uses, at the ...
4
votes
1answer
72 views
What is the connection between extra dimensions in Kaluza-Klein type theories and those in string theories?
This follows to some extent from a question I asked previously about the flaws of Kaluza-Klein theories.
It appears to me that Kaluza-Klein theories attach additional dimensions to spacetime that are ...
2
votes
2answers
73 views
Gauge invariant scalar potentials
If $\Phi$ is a multi-component scalar field which is transforming in some representation of a gauge group say $G$ then how general a proof can one give to argue that the potential can only be a ...
5
votes
2answers
102 views
Why aren't the spin-3/2 fields in the (3/2,0)+(0,3/2) representation?
Why is it that spin-$\frac 32$ fields are usually described to be in the $(\frac 12, \frac 12)\otimes[(\frac 12,0)\oplus(0,\frac 12)]$ representation (Rarita-Schwinger) rather than the $(\frac ...
4
votes
1answer
201 views
A certain gluon scattering amplitude
I am stuck with this process of calculating the tree-level scattering amplitude of two positive helicity (+) gluons of momentum say $p_1$ and $p_2$ scattering into two gluons of negative (-) helicity ...
4
votes
1answer
184 views
Gauge invariance and the form of the Rarita-Schwinger action
in Weinberg Vol. I section 5.9 (in particular p. 251 and surrounding discussion), it is explained that the smallest-dimension field operator for a massless particle of spin-1 takes the form of a field ...
7
votes
1answer
25 views
Low-energy gluodynamics as a string
Does anyone know of a (most likely heuristic) derivation of the use of the string sigma model action to model the soft gluonic interactions between color charges? I'm familiar with the classic ...
9
votes
1answer
40 views
Functional relations for Kochen-Specker proofs
Many proofs of the Kochen-Specker theorem use some form of the following argument (from Mermin's "Simple Unified Form for the major No-Hidden-Variables Theorems" )
[I]f some functional relation
...
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,
$$p_{i_1i_2\ldots i_n}(\theta,\varphi) = \text{Tr}\left \{ \rho ...
13
votes
1answer
109 views
Monte Carlo integration over space of quantum states
I am currently facing the problem of calculating integrals that take the general form
$\int_{R} P(\sigma)d\sigma$
where $P(\sigma)$ is a probability density over the space of mixed quantum states, ...
7
votes
2answers
163 views
Equivalence of definitions of ADM Mass
ADM Mass is a useful measure of a system. It is often defined (Wald 293)
$$M_{ADM}=\frac{1}{16\pi} \lim_{r \to \infty} \oint_{s_r} (h_{\mu\nu,\mu}-h_{\mu\mu,\nu})N^{\nu} dA$$
Where $s_r$ is two ...
10
votes
1answer
452 views
Entanglement in time
Quantum entanglement links particles through time, according to this study that received some publicity last year:
New Type Of Entanglement Allows 'Teleportation in Time,' Say Physicists at The ...
7
votes
0answers
131 views
Magnetic monopole and electromagnetic field quantization procedure
From the Maxwell's equations point of view, existence of magnetic monopole leads to unsuitability of the introduction of vector potential as $\vec B = \operatorname{rot}\vec A$. As a result, it was ...
5
votes
1answer
65 views
Some more questions about the BCFW reduction
This question is a continuation of this previous question of mine and I am continuing with the same notation.
One claims that one can actually split this $n$-gluon amplitude such that there is just ...
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 ...
15
votes
3answers
890 views
Are elementary particles actually more elementary than quasiparticles?
Quarks and leptons are considered elementary particles, while phonons, holes, and solitons are quasiparticles.
In light of emergent phenomena, such as fractionally charged particles in fractional ...
5
votes
0answers
71 views
Instantons and Borel Resummation
As explained in Weinberg's The Quantum Theory of Fields, Volume 2, Chapter 20.7 Renormalons, instantons are a known source of poles in the Borel transform of the perturbative series. These poles are ...
5
votes
3answers
88 views
Analyticity and Causality in Relativity
A few weeks ago at a conference a speaker I was listening to made a comment to the effect that a function (let's say scalar) cannot be analytic because otherwise it would violate causality. He didn't ...
7
votes
0answers
98 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 ...
4
votes
1answer
129 views
The difference between projection operators and field operators in QFT?
Is there a good reference for the distinction between projection operators in QFT, with an eigenvalue spectrum of $\{1,0\}$, representing yes/no measurements, the prototype of which is the Vacuum ...
5
votes
1answer
94 views
Renormalization of the R-charge?
In general I would like to know as to known or what is/are the standard references about R-charge renormalization in supersymmetric theories. When does it do so and what is expected or known to be ...
