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 ...
8
votes
1answer
303 views
Kramer's-Kronig relations for the electron Self-Energy Σ
I'm currently studying an article by Maslov, in particular the first section about higher corrections to Fermi-liquid behavior of interacting electron systems. Unfortunately, I've hit a snag when ...
2
votes
1answer
46 views
Unknown quantum state with promise of classical data
I am trying to solve a problem in the measurement and identification of quantum states with a promise as to what states it could be. Here is the problem. Imagine a system that produces qubits in ...
3
votes
1answer
38 views
A nice overview (and maybe derivation) of the Poincaré transformations of the Vector Spherical Harmonics
With $Y_{lm}(\vartheta,\varphi)$ being the Spherical Harmonics and $z_l^{(j)}(r)$ being the Spherical Bessel functions ($j=1$), Neumann functions ($j=2$) or Hankel functions ($j=3,4$) defining ...
5
votes
1answer
107 views
Some questions about the BCFW reduction
I am trying to give a fast sketch of what the BCFW reduction does and embed within it some questions at the steps which I don't seem to understand clearly. The first bullet point is sort of a very ...
5
votes
2answers
363 views
Feynman rules with helicity states.
Whenever Feynman rules are stated they are always without any mention of the helicities - this I find to be very confusing. How does one introduce and account for that?
Is there an intuitive/simple ...
10
votes
2answers
825 views
Quantum memories: What are they?
Searching the literature for the term "quantum memory" seems to bring up results from two different communities.
On the one hand there are quantum opticians, who see a quantum memory as something ...
5
votes
3answers
32 views
Constructing a CP map with some decaying property
Given some observable $\mathcal O \in \mathcal H$ it is simple to construct a CP (completely positive) map $\Phi:\mathcal{H}\mapsto \mathcal{H}$ that conserves this quantity. All one has to observe is ...
4
votes
0answers
34 views
Status of large-scale structure formation within cosmology today
Since the CMB results of the past decade, would it be fair to say that the consensus among cosmologists is that cosmic strings are no longer considered as a (major) source for density perturbations?
...
11
votes
2answers
70 views
Discussions of the axioms of AQFT
The most recent discussion of what axioms one might drop from the Wightman axioms to allow the construction of realistic models that I'm aware of is Streater, Rep. Prog. Phys. 1975 38 771-846, ...
8
votes
3answers
68 views
Constructing a Hamiltonian (as a polynomial of $q_i$ and $p_i$) from its spectrum
For a countable sequence of positive numbers $S=\{\lambda_i\}_{i\in N}$ is there a construction producing a Hamiltonian with spectrum $S$ (or at least having the same eigenvalues for $i\leq s$ for ...
8
votes
1answer
101 views
Do thermodynamic quantities in CFT correspond to something different in AdS/CFT?
From what I've (hopefully) understood from the AdS/CFT correspondence, physical quantities have a dual version. For example, the position in the bulk is the scale size (in renormalization), and waves ...
7
votes
1answer
88 views
Fourier Methods in General Relativity
I am looking for some references which discuss Fourier transform methods in GR. Specifically supposing you have a metric $g_{\mu \nu}(x)$ and its Fourier transform $\tilde{g}_{\mu \nu}(k)$, what does ...
8
votes
6answers
71 views
Papers and preprints worth reading, Jan-midFeb 2012 [closed]
Which recent (i.e. Jan-midFeb 2012) papers and preprint do you consider really worth reading?
References should be followed by a summary saying what is the result and (implicitly or explicitly) why ...
26
votes
0answers
506 views
What is the upper-limit on intrinsic heating due to dark matter?
Cold dark matter is thought to fill our galactic neighborhood with a density $\rho$ of about 0.3 GeV/cm${}^3$ and with a velocity $v$ of roughly 200 to 300 km/s. (The velocity dispersion is much ...
6
votes
1answer
55 views
Poisson structure on moduli space of CFTs
The moduli space of CFTs with central charge 26 forms the classical phase space of bosonic string theory, in some sense. Similarily the moduli space of SCFTs with central charge 10 forms the classical ...
6
votes
0answers
39 views
Do bipartite spin glasses have simple relaxation dynamics?
From what I gather, a Boltzmann machine (BM) is essentially a spin glass with no applied field evolving under Glauber dynamics (if this is at all mistaken, I don't think it will be off enough to ...
6
votes
1answer
159 views
Thermodynamic limit “vs” the method of steepest descent
Let me use this lecture note as the reference.
I would like to know how in the above the expression (14) was obtained from expression (12).
In some sense it makes intuitive sense but I would ...
4
votes
1answer
69 views
Colour decomposition of $n-$gluon tree amplitude
I have here a $SU(N_c)$ Yang-Mill's theory and let the index $i$, label the $n$-gluons, and $\{k_i, \lambda_i, a_i\}$ be its momenta, helicity and colour index and $\cal{A}_n^{tree/1-loop}(\{k_i, ...
7
votes
4answers
209 views
Different kinds of S-matrices?
It seems to me that the notion of an "S-matrix" refers to several different objects
One construction you can find in the literature is allowing the coupling constant to adiabatically approach 0 in ...
7
votes
3answers
100 views
String-theoretic significance of extended CFT
Extended TQFT and CFT have been puzzling me for while. While I understand the mathematical motivation behind them, I don't quite understand the physical meaning. In particular, it's not clear to me to ...
3
votes
0answers
41 views
Spectrum of a quantum relativistic “distance squared” operator
This question disusses the same concepts as that question (this time in quantum context). Consider a relativistic system in spacetime dimension $D$. Poincare symmetry yields the conserved charges $M$ ...
6
votes
3answers
762 views
Interesting topics to research in mathematical physics for undergraduates
I'm planning on getting into research in mathematical physics and was wondering about interesting topics I can get into and possibly make some progress on.
I'm particularity fond of abstract algebra ...
9
votes
1answer
168 views
Derivation of the effective potential between a quark and an anti-quark
Typically in particle physics books (not in QFT books!) I have often seen this statement that the potential between a heavy quark and its anti-quark can be "empirically" represented as $V(r) = ...
6
votes
1answer
86 views
random matrix ensembles from BMN model
My friends working on Thermalization of Black Holes explained solutions to their matrix-valued differential equations (from numerical implementation of the Berenstein-Maldacena-Nastase matrix model) ...
3
votes
1answer
69 views
Random bond Ising model and computational efficiency
If you want to find the ground state of the 2d random bond Ising model (no field), a computationally efficient algorithm exists to do it for you (based on minimum weight perfect matching). What about ...
9
votes
1answer
154 views
Reduced density matrices for free fermions are thermal
Many recent papers study entanglement in eigenstates of fermionic free hamiltonians (normally on a lattice) using the basic assumption that the reduced density matrices are thermal (e.g. Peschel ...
16
votes
1answer
230 views
Why is there no theta-angle (topological term) for the weak interactions?
Why is there no analog for $\Theta_\text{QCD}$ for the weak interaction? Is this topological term generated? If not, why not? Is this related to the fact that $SU(2)_L$ is broken?
8
votes
1answer
73 views
Many body quantum states analyzed as probabilistic sequences
Measurements of consecutive sites in a many body qudit system (e.q. a spin chain) can be interpreted as generating a probabilistic sequence of numbers $X_1 X_2 X_3 \ldots$, where $X_i\in ...
3
votes
2answers
96 views
Do any entanglement measures for mixed states exist that use only single site correlation functions?
For a pure state $\rho_{AB}$, the entropy of entanglement of subsystem $A$ is
\begin{equation}
S( \rho_A) = -tr (\rho_A \log \rho_A)
\end{equation}
where $\rho_A$ is the reduced density matrix of A. ...
5
votes
2answers
234 views
Some questions about Wilson loops
Let $G$ be the gauge group whose Yang-Mill's theory one is looking at and $A$ be its connection and $C$ be a loop in the space-time and $R$ be a finite-dimensional representation of the gauge group ...
3
votes
1answer
146 views
An odd relation with the epsilon/delta invariant tensors of SO(3)
The rotation group SO(3) can be viewed as the group that preserves our old friends the delta tensor $\delta^{ab}$ and $\epsilon^{abc}$ (the totally antisymmetric tensor). In equations, this says:
...
7
votes
1answer
255 views
Relativistic center of mass
Recently I realized the concept of center of mass makes sense in special relativity. Maybe it's explained in the textbooks, but I missed it. However, there's a puzzle regarding the zero mass case
...
4
votes
0answers
48 views
functional representations of free quantum fields
The free real quantum field, satisfying $[\hat\phi(x),\hat\phi(y)]=\mathrm{i}\!\Delta(x-y)$, $\hat\phi(x)^\dagger=\hat\phi(x)$, with the conventional vacuum state, which has a moment generating ...
11
votes
3answers
133 views
POVMs that do not require enlargement of the Hilbert space
The usual justification for regarding POVMs as fundamental measurements is via Neumark's theorem, i.e., by showing that they can always be realized by a projective measurement in a larger Hilbert ...
9
votes
1answer
277 views
Boundary conditions / uniqueness of the propagators / Green's functions
My question(s) concern the interpretation and uniqueness of the propagators / Green's functions for both classical and quantum fields.
It is well known that the Green's function for the Laplace ...
18
votes
2answers
160 views
Values of SM parameters at one certain scale
The general question is:
What are the values of Standard Model parameters (in the $\bar{MS}$ renormalization scheme) at some scale e.g. $m_{Z}$? As its parametrization in Yukawa matrices is not unique ...
9
votes
1answer
74 views
How can one build a multi-scale physics model of fluid flow phenomena?
I am working on a problem in Computational Fluid Dynamics, modeling multi-phase fluid flow through porous media. Though there are continuum equations to describe macroscopic flow (darcy's law, ...
6
votes
0answers
46 views
Pohlmeyer reduction of string theory for flat and AdS spaces
The definition of Pohlmeyer invariants in flat-space (as per eq-2.16 in Urs Schreiber's DDF and Pohlmeyer invariants of (super)string) is the following:
$ Z^{\mu_1...\mu_N} (\mathcal{P}) = ...
6
votes
3answers
161 views
Modular invariance for higher genus
As far as I understand, there are roughly 2 "common" kinds of 2D conformal field theories:
Theories that are defined only on the plane, more precisely, on any surface of vanishing genus. Such a ...
3
votes
0answers
125 views
Stability of the vacuum state of interacting quantum fields
"Stability" is generally taken to be the justification for requiring that the spectrum of the Hamiltonian should be bounded below. The spectrum of the Hamiltonian is not bounded below for thermal ...
5
votes
2answers
84 views
Torsion and gauge invariant EM kinetic term
Everytime I hear about adding torsion to GR, something struggles me: how do you create a kinetic term for the electromagnetic field that is still gauge-invariant? One of the consequences of torsion is ...
8
votes
2answers
131 views
Wilson Loops in Chern-Simons theory with non-compact gauge groups
VEVs of Wilson loops in Chern-Simons theory with compact gauge groups give us colored Jones, HOMFLY and Kauffman polynomials. I have not seen the computation for Wilson loops in Chern-Simons theory ...
8
votes
1answer
174 views
Derivation of the basic equation for Witten diagrams
I could understand the derivation of the "bulk-to-boundary" propagators ($K$) for scalar fields in $AdS$ but the iterative definition of the "bulk-to-bulk" propagators is not clear to me.
On is ...
6
votes
0answers
49 views
String landscape in different dimensions
For D = 11 large (uncompactified) spacetime dimensions, the only "string theory" vacuum is M-theory
For D = 10, there are 5 vacua. Or maybe it's more correct to say 4, since type I is S-dual to ...
6
votes
1answer
140 views
Uniqueness of the 5 string theories
This question combines several sub-questions, the common theme being: why the known 5 string theories are unique?
Firstly, regarding heterotic theory. I understand the only allowed gauge groups are ...
38
votes
2answers
576 views
Analog Hawking radiation
I am confused by most discussions of analog
Hawking radiation in fluids (see, for example,
the recent experimental result of Weinfurtner et
al. Phys. Rev. Lett. 106, 021302 (2011), ...
7
votes
0answers
164 views
Information geometry of 1D Ising model in complex magnetic field regime
Consider the one-dimensional Ising model with constant magnetic field and node-dependent interaction on a finite lattice, given by
$$H(\sigma) = -\sum_{i = 1}^N J_i\sigma_i\sigma_{i + 1} - h\sum_{i = ...
11
votes
1answer
205 views
Lagrangian for Euler Equations in general relativity
The stress energy tensor for relativistic dust
$$
T_{\mu\nu} = \rho v_\mu v_\nu
$$
follows from the action
$$
S_M = -\int \rho c \sqrt{v_\mu v^\mu} \sqrt{ -g } d^4 x
= -\int c \sqrt{p_\mu ...
11
votes
1answer
81 views
Some questions on a version of the O'Raifeartaigh model
This form is taken from a talk by Seiberg to which I was listening to,
Take the Kahler potential ($K$) and the supersymmetric potential ($W$) as,
$K = \vert X\vert ^2 + \vert \phi _1 \vert ^2 + ...
16
votes
3answers
143 views
Regularization of the Casimir effect
For starters, let me say that although the Casimir effect is standard textbook stuff, the only QFT textbook I have in reach is Weinberg and he doesn't discuss it. So the only source I currently have ...
