Questions tagged [research-level]
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 questions should not require new or groundbreaking research and results to answer.
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How to transform a given Lagrangian to a Nambu-Gorkov basis?
With reference to the Nambu (or famously, Nambu-Gorkov) transformation in this paper, could someone explain the reason behind using the 3rd Pauli matrix in the Lagrangian after equation (2.3) (would ...
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Are Chern-Simons theories classified by bordism groups?
For a long time it was thought that anomalies for a group $G$ were classified by $H^n(BG)$, although it is now understood that they are in fact classified by $\Omega^n(BG)$.
On the other hand, ...
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Waves on a topological surface
Are there any formulas for wave motion on a topological surface, like a Mobius strip? If not, is this a valid opportunity for research?
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Renormalization Group for non-equilibrium
For equilibrium/ground state systems, a (Wilson) renormalization group transformation
produces a series of systems (flow of Hamiltonians/couplings $H_{\Lambda}$ where $\Lambda$ is the cut-off) such ...
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What compactifications of the Poincaré group have been studied?
As we know, the Poincaré group is non-compact. Poincaré invariance has been observed at velocities and energies up to $10^{20}$ eV in cosmic rays. The other day, I was thinking about how the $SU(2)$ ...
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By how much are various dibaryon states unbound?
It has been known for a long time that the deuteron is stable but the dineutron (nn) and diproton (pp) are not. Many textbooks comment on this, but all the ones I found so far do not give quantitative ...
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Deriving Drude Theory from Plasma Fluid Equations
Does anyone have experience in looking at Drude theory from the perspective of plasma physics instead of the standard, condensed-matter, "electrons in a metal" sort of thing and can point ...
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Bogomol'nyi-Prasad-Sommerfield (BPS) states: Mathematical definition
What is the proper mathematical definition of BPS states?
In string theory the BPS states correspond either to coherent sheaves or special Lagrangians of Calabi-Yau manifold depending upon the type of ...
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The $I_{3322}$ Inequality
I am trying to understand the $I_{3322}$ inequality which is an another example of Bell inequalities and which is different from the famous CHSH inequality. I haven't got hold of any standard ...
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String theory from a mathematical point of view
I have a great interest in the area of string theory, but since I am more focused on mathematics, I was wondering if there is any book out there that covers mathematical aspects of string theory. I ...
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The phrase "Trace Anomaly" seems to be used in two different ways. What's the relation between the two?
I've seen the phrase "Trace Anomaly" refer to two seemingly different concepts, though I assume they must be related in some way I'm not seeing.
The first way I've seen it used is in the manner, for ...
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Matrix Model in AdS/CFT & exact results
Matrix models appeared in the context of AdS/CFT while trying to calculate the Circular Wilson Loop. It was first noted by Erickson, Semenoff & Zarembo [hep-th/0003055] that the 2-loop ...
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Pseudocubic unit cells: how to construct one?
I keep coming across the term pseudocubic unit cell while reading about orthorhombic perovskite structures. No clear explanation ...
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How to get algebraic PSG solutions once we got the constraints?
The question is more technical than conceptual. I've been trying to understand the classification of spin liquids as done by Prof.Wen. I have got the constraints on IGG(Invariant gauge group) elements ...
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Gauge symmetry is not a symmetry?
I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate ...
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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 $G$...
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Energy of states in non-equilibrium systems
In equilibrium thermodynamics, the Boltzmann distribution gives the probability of finding a system in a certain $i$: $P_i = e^{-\frac{E_i}{k_B T}}$. Conversely, by measuring state probabilities one ...
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Global anomaly for discrete groups
We know that:
a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformations that would otherwise be preserved in the ...
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Constructing W-algebras
I am following the algorithm in W-algebras with two and three generators, in order to construct consistent (anti-)commutator relations for a particular W-algebra.
I am considering $W(2,4,4)$ where ...
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Origin an realization of 2D magnetic materials
Recently, I encountered 2D magnetic materials. At first, I was a little bit surprised by the fact that one can have a 2D magnetic material because I thought of Mermin-Wagner's theorem, which states ...
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What are the quantum dimensions of the primary fields for $SU(N)$ level-$k$ Kac-Moody current algebras?
The CFT of the $\mathrm{SU}(N)$ level $k$ Kac-Moody current algebra has many Kac-Moody primary fields. I wonder if any one has calculated the quantum dimensions of those Kac-Moody primary fields.
I ...
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How many Anyons can be allowed in a state
For fermions, a state allows only one fermion to exist . For bosons, there can be infinite number of bosons in one state . But for anyons, how many can a state allow?How do we come to this conclusion?
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What classifies gaugings?
Gauging a global symmetry $G$ introduces several free parameters to the theory. For example,
In $d=4$, gauging a simple and simply-connected Lie group introduces a coupling constant and a theta term, ...
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Why isn't the Gear predictor-corrector algorithm for integration of the equations of motion symplectic?
Okumura et al., J. Chem. Phys. 2007 states that the Gear predictor-corrector integration scheme, used in particular in some molecular dynamics packages for the dynamics of rigid bodies using ...
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What are the efficient ways of reading a physics research paper, understand and come up with new ideas? [closed]
I am planning to do research in theoretical particle physics and phenomenology. But as opposed to reading a textbook, I find that understanding journal papers to complete satisfaction could be quite ...
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Where do theta terms live?
Consider a gauge theory with group $G$. The canonical kinetic term for the gauge field is $F\wedge\star F$ and, depending on the dimensionality of spacetime, there are other allowed terms, such as ...
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Which CFTs have AdS/CFT duals?
The AdS/CFT correspondence states that string theory in an asymptotically anti-De Sitter spacetime can be exactly described as a CFT on the boundary of this spacetime.
Is the converse true? Does any ...
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Gauge group R and U(1) and a global symmetry
In the beautiful paper by Harlow et Ooguri, they write in section 2.1 about this action
$$ S=-\frac12 \int_M F_a \wedge \star F_b \delta^{ab}\;, $$
with index $a=1,2$. They say that if the gauge ...
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dS/CFT in a positive curvature universe
Since Maldacena ground breaking theoretical discovery, have there been any succesfull efforts to try to transpose the AdS/CFT duality to our universe (not an AdS)?
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What is the role of metric transitivity in statistical mechanics?
I was reading a paper of E.T. Jaynes 'Information Theory and Statistical Mechanics'. There he mentions the following principle in the section 'Application to Statistical Mechanics':
The link to paper
...
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Sigma Models on Riemann Surfaces
I'm interested in knowing whether sigma models with an $n$-sheeted Riemann surface as the target space have been considered in the literature. To be explicit, these would have the action \begin{align*}...
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Electric potential of a spheroidal gaussian
I'm looking for results that compute the electrostatic potential due to a spheroidal gaussian distribution. Specifically, I'm looking for solutions of equations of the form
$$
\nabla^2\Phi=N\exp\left({...
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Isn't Big Bang theory a violation of law of conservation of linear momentum?
What Big Bang theory assumed in the formation of universe?
Answer:-At its simplest, it says the universe as we know it started with a small singularity, then inflated over the next 13.8 billion ...
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If a particle can exert a force on itself,then can we define a whole lot of newtonian mechanics corresponding to it?
I think that it may be a broad question to be answered but if small amount of discussion is possible then it would be very helpful for all of us.
Basically,I asked a question on this website a few ...
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Calculate the matrix size for ground states BEC using difference with Gross–Pitaevskii equation
The Ground states BEC at $0$ temperature can be described by Gross–Pitaevskii equation as
$(-\frac{\hbar^2}{2m}\nabla^2+V(r)+g|\psi|^2)\psi(r)=\mu\psi(r)$
We limit the BEC in 2D where $V(r)=\frac{1}{...
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Adiabatic theorem and Berry phase
As far as I can check, the adiabatic theorem in quantum mechanics can be proven exactly when there is no crossing between (pseudo-)time-evolved energy levels. To be a little bit more explicit, one ...
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Comparision of using two dimensional mode or one dimensional in case of optical data transmission
Many works have been done to increase capacity of optical communication. I saw that some researcher using 1-D mode ,some 2-D to implement their device.The reson of using 1-d/2-d beacuse of their types ...
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Role of pure mathematics in fusion?
Is there any way a pure math guy can get his rigorous math fix while simultaneously moving fusion research forward? Is fusion simply too complicated to take a pure math approach? What open math ...
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What is the relationship of optical mode and data?
This question is on the plot of mode division multiplexing system where it is said capacity crunch can be solved using mdm technique. Now, we know single mode fiber can transmit upto 1Tbps. Now if i ...
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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 ...
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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 ...
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Metric interpretation of self-adjoint extensions?
I am wondering if beyond physical interpretation, the one dimensional contact interactions (self-adjoint extensions of the the free Hamiltonian when defined everywhere except at the origin) have a ...
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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 $...
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What are some critiques of Jaynes' approach to statistical mechanics?
Suggested here: What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis?
I was wondering about good critiques of Jaynes' approach to statistical ...
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How does physics research work? [closed]
I am going to try and be as short and as concise as possible.
I was thinking these last few days about how we're still trying to discover a unified Theory of Everything.
The question is: how is this ...
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Vandermonde determinant factor in supersymmetric gauge localisation computation
I am trying to learn supersymmetric localisation computation in which the path integral of a supersymmetric gauge theory (placed on a sphere) can be localised exactly to a BPS configuration ...
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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 ...
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How exactly does a spin TQFT depend on the spin structure?
Take a spin Chern-Simons TQFT, such as $U(N)$ or $SO(N)$ with odd level. Such system depends on the spin structure of the underlying manifold.
But how exactly does the theory depend on the spin ...
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Can you do gauge theories over topological groups?
Quantum gauge theories involve (functional) integration over a Lie group. Is there any meaningful generalisation to (non-manifold) topological groups?
Consider for example the Whitehead tower
$$
\...
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What is the topological data for $(\mathbb Z_n)_p$ theories?
Consider the 3d TQFT described by the Lagrangian (Dijkgraaf-Witten with gauge group $\mathbb Z_n$ at level $p$):
$$
\mathcal L=\frac{n}{2\pi} B\wedge\mathrm dA+\frac{p}{4\pi}A\wedge\mathrm dA
$$
with $...