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2
votes
1answer
536 views

QCD color factors from quark gluon vertices

The color factors in QCD tell us the relative strength of the coupling of a quark emitting a gluon, a gluon emitting a quark-antiquark pair or a gluon emitting two gluons. To calculate let them we ...
2
votes
1answer
283 views

Atomic nearest neighbor notation

I recently got a correction to a paper that I am writing. The correction references a section in which I talk about nearest neighbors. The comment says: Do you mean NN, NNN, etc., or NN, 2NN, 3NN? ...
2
votes
1answer
168 views

Reaction coordinate as a function of atomic positions

I'm going over some (molecular dynamics) related literature - specifically the derivation of the Weighted Histogram Analysis Method (WHAM). As a quick backdrop WHAM is a method for stitching ...
0
votes
1answer
21 views

Klein-Gordon equation probability density and current

After multiplying the K-G equation and its conjugate by the field, I have this equation $$\phi^*\frac{\partial^2 \phi}{\partial t^2}- \phi\frac{\partial^2 \phi^*}{\partial t^2}+\phi ...
0
votes
1answer
47 views

Is the unit symbol written twice when using the +\- symbol?

When notating error using the $\pm$ symbol, are the units only ever included at the end? For example: 10.2 $\pm$ 3.2 m rather than 10.2 m $\pm$ 3.2 m This seems to be correct though I ...
-1
votes
1answer
44 views

What does $\bar{x}_{\textrm{el}}$ represent?

In the context of centroids and moments, what do $\bar{x}_{\textrm{el}}$ and $\bar{y}_{\textrm{el}}$ represent? For example: $$\bar{x}L = \int \bar{x}_{\textrm{el}}dL$$ Some references that use ...
5
votes
0answers
148 views

Is it correct to sum over either index of the metric the same way?

I don't know if the following is correct, i want to compute the following derivative $$\frac{\partial }{\partial (\partial_{\mu}A_{\nu})}\left(\partial^{\alpha}A^{\beta}\partial_{\alpha}A_{\beta} ...
4
votes
0answers
39 views

What is $\mathrm{U(1)}$ vector and axial?

In hadron physics we talked about $\mathrm{U(1)_V}$ (vector) and $\mathrm{U(1)_A}$ (axial) as well as $\mathrm{SU(3)_L}$ (left) and $\mathrm{SU(3)_R}$ (right). There are certain relations between them ...
4
votes
0answers
102 views

What decides the signs and coefficients of terms in superfield?

I'm working on a problem in 3d field theory and I'm confused about how to write the superfields. Specifically, I'm not sure if the signs and coefficients of terms are purely a matter of convention or ...
3
votes
0answers
123 views

The states of the adjoint representation correspond to the generators

I understand the definition of the adjoint representation. It uses structure constants as matrix components of generators, but I can't understand meaning of the states $|X_{a}\rangle$. What does ...
3
votes
0answers
158 views

Topological quantum computation : Anyon model

Could someone tell me about Frobenius-Schur indicator and the associated cups and caps notation in context of anyon model. One possible reference could be Parsa Bonderson thesis which is freely ...
3
votes
0answers
179 views

Group theory notation used in physics (AdS/CFT)

This in the context of the AdS/CFT correspondence. I am reading this review on AdS/CFT Aharony et. al. (The MAGOO review) The abstract can be found here Equation (2.50) of the above paper lists the ...
2
votes
0answers
22 views

What is the origin of the naming convention for the various branches in vibration-rotational spectroscopy?

In vibration-rotational spectroscopy, the different spectral lines are grouped into branches for different changes in the total angular momentum, i.e. $$ \begin{array}{rrrrrr} & \mathrm{O} & ...
2
votes
0answers
30 views

Nomenclature of nuclear excited states

I read in an online portal about $^{112}$Sn nucleus making a transition from $0_{g.s}^{+} \rightarrow 2_{1}^{+}$ state. Also, some higher excited states were named as $0_{2}^{+}$, $3_{1}^{-}$, etc. ...
2
votes
0answers
41 views

Atomic physics, determining levels and terms

In atomic physics I understand there a configurations, terms and levels. I think levels for instance appear because of spin-orbit interactions, so that terms are split. But I'm confused about the ...
2
votes
0answers
88 views

Index notation for a Lagrangian with second derivatives

I'm finding the field equations for a hypothetical Lagrangian with dependence on the second derivative of a scalar field, $L\left(\phi,\phi_{,\mu},\phi_{,\mu\nu}\right)$, and in the analogue to the ...
2
votes
0answers
32 views

Vibrational quantum notation

Reading articles on spectroscopy I often see this notation: 30001 <- 01101, 00011 <- 00001 in context of molecular ...
2
votes
0answers
142 views

Convention in physics for [],{} and operators (QM)

I got a little mixed up with the convention in physics. Usually a hat means an operator. For a given electron-ion Hamiltonian $\hat{H}_{e-n}$, what are the difference between these: 1) ...
1
vote
0answers
55 views

Is $d^3r$ the same as $dV$, the volume element?

I've seen the term $d^3r$ being used instead of $dV$. Are they exactly the same? Do they have a different connotation?
1
vote
0answers
103 views

Perturbation theory, eigenvalues and eigenvectors for degenerate case (1st order)

I was trying to understand the perturbation theory, but I was lost in the notation... I have understood that I have to identify the unperturbed kets that are degenerated and find the matrix $V$, ...
1
vote
0answers
85 views

Notation - d.o.f.'s for Grassmann delta functions in a SUSY field theory amplitude

I was reading the following paper http://arxiv.org/pdf/1306.2962v1.pdf as I stumbled upon an issue concerning counting and assigning the Grassmann degrees of freedom that appear in grassmann delta ...
1
vote
0answers
51 views

Are derivative indices summed in indicial notation?

A paper I'm reading uses indicial notation and the convention that $u_{j,k}$ means the derivative with respect to $x_k$. Which one of these interpretations are correct? $$A_{ijk}u_{j,k} = ...
1
vote
0answers
326 views

Field Strength Renormalisation in Peskin and Schroeder

In chapter 7 of Peskin and Schroeder they define the field strength renormalisation $Z$ for a quantum field to be the residue of the Fourier transform of the correlation function $$\langle \Omega | ...
0
votes
0answers
25 views

Index Placement for Spinors in Relativity

This may ultimately be a silly question, but a pedantic mind like mine gets tied into knots over differing notation. (Disclaimer: I'm a mathematician.) Let $\mathbb{W}$ be a complex two-dimensional ...
0
votes
0answers
49 views

QFT Normalization of multi-particle states

Peskin 7.2 states that the identity operator for the entire Hilbert space is given by ...
0
votes
0answers
143 views

Definition of Hamilton operator

The Hamilton operator is by definition a self-adjoint operator $H\text{: }D\left(H\right)\to\mathcal{H}$ with $D\left(H\right)\subset\mathcal{H}$ a dense linear subspace of the Hilbert space ...
0
votes
0answers
132 views

What is the meaning of symbols $\delta f$ and $\delta^2f$?

Professor was using these symbols to derive the continuity equation. He defined the infinitesimal mass as $\delta^2m=\rho \delta V$ and the mass that leaves some closed boundary $\partial V$ as ...
0
votes
0answers
42 views

Is it ever appropriate to write $| \phi(t)>$

I am trying to solve the Schrodinger's wave equation $\hat H |\psi(x,t)> = E|\psi(x,t)>$ using separation variables so that $\psi(x,t) = \psi(x)\phi(t)$ Solving the equation involves the step ...
0
votes
0answers
20 views

Proper nuclear reaction notation for arbitrary species

I am wondering the common way to write a nuclear reaction for an arbitrary species. For instance, for neutron capture on a species $X$: $$^{A}_ZX + n \rightarrow ^{A+1}_{\ \ \ \ \ Z}X'.$$ Is this ...
0
votes
0answers
157 views

Index Notation Double Curl

My question is about Einstein notation. It does not matter the specifics of this example (the del operator could be another random vector), I just want to know if my assumption about notation is ...
0
votes
0answers
78 views

How should the implicit sum $C_{ijkl}u_{i,j}u_{k,l}$ be interpreted?

$C$ is a 3x3x3x3 tensor. How should the expression $C_{ijkl}u_{i,j}u_{k,l}$ be interpreted? This is my guess: $$ \sum_{i=1}^3\sum_{j=1}^3 \sum_{k=1}^3\sum_{l=1}^3 C_{ijkl}u_{i,j}u_{k,l} $$
0
votes
0answers
188 views

Quantum Mutual Information scaling

Wikipedia provides a simple definition of Quantum Mutual Information: $$I(\rho^{ab})= S(\rho^{a}) + S(\rho^{b}) - S(\rho^{ab})$$ where in terms of relative information we have: $$I(\rho^{ab})= ...