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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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 ...
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4answers
482 views
What exactly does the holographic principle say?
Does the holographic principle say given a spatially enclosing boundary satisfying the Bousso condition on expansion parameters, the log of the number of microstates in its interior is bounded by ...
7
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1answer
49 views
Canonical averages in a Fermi gas aka generalized Fermi-Dirac distribution
I am in the process of applying Beenakker's tunneling master equation theory of quantum dots (with some generalizations) to some problems of non-adiabatic charge pumping. As a part of this work I ...
7
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1answer
46 views
Matrix geometry for F-strings
A stack of N D-branes has the strange property that the traverse D-brane coordinates are matrix-valued. When the matrices commute, they can be interpreted as ordinary coordinates for N ...
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1answer
193 views
Canonical quantization in supersymmetric quantum mechanics
Suppose you have a theory of maps
$\phi: {\cal T} \to M$
with $M$ some Riemannian manifold,
Lagrangian
$$L~=~ \frac12 g_{ij}\dot\phi^i\dot\phi^j + \frac{i}{2}g_{ij}(\overline{\psi}^i ...
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1answer
166 views
Are Born-Oppenheimer energies analytic functions of nuclear positions?
I am looking for references to bibliography that explores the smoothness and analyticity of eigenvalues and eigenfunctions (and matrix elements in general) of a hamiltonian that depends on some ...
7
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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 ...
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2answers
119 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 ...
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1answer
141 views
Parton showering in Pythia 6 Monte Carlo generator
I have Pythia Monte Carlo (MC) samples where I can't understand the parton showering model. If I print out full decay chains from the events, each event contains multiple string objects with pdgId 92. ...
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1answer
175 views
What is the generalization, if any, of the weak and dominant energy conditions to SUGRA?
In standard general relativity, we have the null energy condition, the weak energy condition related to stability, and the dominant energy condition related to forbidding superluminal causal ...
7
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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
...
7
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1answer
78 views
Characters of $\widehat{\mathfrak{su}}(2)_k$ and WZW coset construction
I am currently studying affine Lie algebras and the WZW coset construction. I have a minor technical problem in calculating the (specialized) character of $\widehat{\mathfrak{su}}(2)_k$ for an affine ...
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0answers
133 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 ...
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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 = ...
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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 ...
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0answers
110 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, ...
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0answers
53 views
Quantum statistics of branes
Quantum statistics of particles (bosons, fermions, anyons) arises due to the possible topologies of curves in D-dimensional spacetime winding around each other
What happens if we replace particles by ...
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0answers
284 views
Measurement of Tangential Momentum Accomodation?
(this question is a crosspost from theoretical physics.)
I am using atomic force microscopy (AFM) for characterizing
pores of the size of nanometers for application in gas flow. For
this, knowing ...
6
votes
2answers
174 views
How to prove quantum N=4 Super-Yang-Mills is superconformal?
I'm especially interested in elegant illuminating proofs which don't involve a lot of straightforward technical computations
Also, does a non-perturbative proof exist?
6
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1answer
66 views
what compactifications of the Poincare group have been studied?
as we know the Poincare group is non-compact. Poincare invariance have been observed in velocities and energies up to $10^{20}$ eV in cosmic rays. The other day i was thinking in how $SU(2)$ ...
6
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1answer
42 views
Allowed states vis-a-vis allowed dynamics in generalized probabilistic theories (GPTs)
In his work on information processing in GPTs http://arxiv.org/abs/quant-ph/0508211 Barrett speculates that the trade-off between allowed states and the allowed dynamics in a GPT is optimal in quantum ...
6
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1answer
69 views
Quantum mechanics as a Markov process
I am currently involved in some understanding on this matter with a colleague of mine. I know all the literature about but I do not know the state of art. Please, could you provide some relevant ...
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3answers
763 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 ...
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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
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2answers
54 views
Infinity of running couplings
A Landau pole - an infinity occurring in the running of coupling constants in QFT is a known phenomena. How does the Landau pole energy scale behave if we increase the order of our calculation, (more ...
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2answers
284 views
Is there a published upper limit on the electron's electric quadrupole moment?
I understand an electric quadrupole moment is forbidden in the standard electron theory. In this paper considering general relativistic corrections (Kerr-Newman metric around the electron), however, ...
6
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1answer
81 views
Quantum mechanical gravitational bound states
The quantum mechanics of Coloumb-force bound states of atomic nuclei and electrons lead to the extremely rich theory of molecules. In particular, I think the richness of the theory is related to the ...
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1answer
74 views
Scherk-Schwarz and other compactifications?
I have been thinking about various types of compactifications and have been wondering if I have been understanding them, and how they all fit together, correctly.
From my understanding, if we want ...
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1answer
96 views
Status of the little hierarchy problem
What is the current thinking on the little hierarchy problem in light of a potential Higgs mass above 120 GeV? A few years ago, at least, I remember various phenomenologists saying that this at least ...
6
votes
1answer
50 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
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 ...
6
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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 ...
6
votes
2answers
35 views
Charged black holes in equilibrium
Consider a pair of (possibly rotating) charged black holes with masses m1, m2 and like charges q1, q2. It seems that under certain conditions gravitational attraction should exactly cancel ...
6
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1answer
111 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 ...
6
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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 ...
6
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1answer
43 views
Which arguments for $m_u \approx 0$ are still in the market?
The RPP note on quarks masses has traditionally carried, and it is still there, the comment that
It is particularly important to determine the quark mass ratio mu/md,
since there is no strong CP ...
6
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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
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1answer
98 views
Forcing quadrupole moments to vanish for a neutral system
For a system of electric charges $q_i$, at positions $\mathbf{r}_i$, with a nonzero net charge $Q=\sum_i q_i$, one can define a "centre of charge" in the obvious way as
$$
...
6
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1answer
156 views
Spin-ice materials with strong quantum fluctuations
Spin-ice materials are insulating materials where
spins form a 3D pyrochlore lattice and have a frustrated magnetic interaction. The spin dynamics in most spin-ice materials
is very classical and has ...
6
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1answer
43 views
How does a geodesic equation on an n-manifold deal with singularities?
My general premise is that I want to investigate the transformations between two distinct sets of vertices on n-dimensional manifolds and then find applications to theoretical physics by:
...
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1answer
427 views
Definition and difference between the R-symmetry and the $U(1)_R$ internal symmetry
For a general ${\cal N}$ the R-symmetry group is $U({\cal N})$ but for the ${\cal N}=2$ case why is it $SU(2)$ ? I guess it is again different for ${\cal N}=4$. How does one understand this?
One ...
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1answer
162 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 ...
6
votes
1answer
268 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 ...
6
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1answer
89 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 ...
6
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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 ...
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) ...
6
votes
1answer
149 views
Chiral coupling in string-nets
In Xiao-Gang Wen's review of topological order http://arxiv.org/abs/1210.1281 , he states in footnote 52 that string-nets are so far unable to produce the chiral coupling between the SU(2) gauge boson ...
6
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1answer
300 views
Realization of Witten-type topological quantum field theory in condensed matter physics
It is well-known that some exotic phases in condensed matter physics are described by Schwarz-type TQFTs, such as Chern-Simons theory of quantum Hall states. My question is whether there are condensed ...
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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}) = ...
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0answers
20 views
status of +4/3 scalar as explanation of $t\bar t$ asymmetry
One of the early proposals for the Tevatron asymmetry on $t \bar t$ was a "fundamental diquark" with a charge (and hypercharge) +4/3, either in a triplet or a sextet colour. I am interested on the ...
