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2answers
183 views

Understanding basic quantum mechanics notation

I was talking with a guy about energy levels of an atom in a magnetic field. He said that energy levels are shifted and that, if you want know how much, you have to analyze this: for 1s state: ...
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1answer
204 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
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1answer
138 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 ...
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1answer
38 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 ...
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0answers
128 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} ...
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0answers
95 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
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0answers
135 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) ...
3
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0answers
96 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
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0answers
156 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
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0answers
22 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
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0answers
43 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
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0answers
131 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 ...
1
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0answers
31 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 ...
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0answers
22 views

Vibrational quantum notation

Reading articles on spectroscopy I often see this notation: 30001 <- 01101, 00011 <- 00001 in context of molecular ...
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0answers
100 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 ...
1
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0answers
47 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
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0answers
235 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 | ...
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0answers
39 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 ...
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0answers
17 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 ...
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0answers
61 views

Coordinate Symbol confusion in general relativity

In a previous post (Finding the metric tensor from the Einstein field equation?), the equation used lambda, rho mu and nu (not sure of the names of the letters!) for the Ricci tensor and swapped to a, ...
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0answers
20 views

Need Quick reference card for scientific notation and symbols for paper reading

Hi can any one lead me to resource for symbols and notation and their meaning used for writing/publishing/scientific writing paper eg: Δ or δ means difference . ∀ means 'for all' x | y pipe mean ...
0
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0answers
46 views

How to read this state in quantum physics?

I am having a little trouble understanding this state: $$ \,^3D\left[3/2\right]_{1/2} $$ What does the $[3/2]$ indicate here?
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0answers
71 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: $$ \sum_{i=1}^3\sum_{j=1}^3 \sum_{k=1}^3\sum_{l=1}^3 C_{ijkl}u_{i,j}u_{k,l} $$
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0answers
153 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})= ...