Category Archives: physics

Tutorial on translating particle physics effective Lagrangians to conventional atomic physics and quantum chemistry operators

Occasionally we have to carry out calculations with some effective Lagrangians
supplied by our particle physics friends (possibly related to new physics
beyond the standard model). For example, we could be given a Lagrangian density


where is some scalar field, is the Dirac field (electrons) and is a coupling constant. The Dirac equation that is conventionally used in atomic physics reads

(I suppress interactions of electrons with each other and with the nucleus). Given what is that extra operator that I would have to add to my Dirac Hamiltonian? I consistently derive in this tutorial (pdf).

For the impatient, the result is \begin{equation}
V^{\prime}\psi=-\gamma_{0}\left( \frac{\partial\mathcal{L}^{\prime}}
{\partial\bar{\psi}}-\partial_{\mu}\left( \frac{\partial\mathcal{L}^{\prime}
}{\partial\left( \partial_{\mu}\bar{\psi}\right) }\right) \right) .
\end{equation} Applications to axions and "Higgs portal" interactions are also covered in the tutorial (pdf).

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Collaborative tools of the trade

I think you would agree that with recent introduction of cloud services collaboration has become easier.  Ftp/sftp/scp have become nearly obsolete. Here is a couple of tools that we find useful:

  1. Dropbox. This is a cloud file service. The first 2 Gb (which is a lot) are free. An essential tool for sharing projects between group members. Indispensible for  synchronizing files across various platforms, PCs, Macs, smartphones, ipads, etc. Five out of five stars.
  2. Mendeley. Bibliography manager. Free. Multiplatform. We share citations and papers (pdf's) between group members; anyone can add and modify references. Mendeley has a convenient option for exporting bibliography into latex .bib file (library.bib). At the moment flaky but still useful. Three out of five stars.

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Setting working directory in mathematica

One of mathematica annoyances when working with external files (various import/export functions), is that it defaults to the user's Documents directory. I usually keep the data/graphics files  in the same directory as the mmka notebook and its painful to specify the full path every time.

Here is a command that sets the working directory to the notebook directory.

SetDirectory[
DirectoryName[
ToFileName["FileName" /. NotebookInformation[SelectedNotebook[]]]]]

UPDATE: Easier (thanks Pedro!):
SetDirectory@NotebookDirectory[]

 

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Tweaking Mathematica output for order-of-magnitude estimates

Here is a trick I find useful when quickly estimating order-of magnitude values of various quantities  in Mathematica. The statements below force the format of all numerical output to be in the scientific notation (x 10^y).

oldPost = $Post;
format[x_Real] :=
NumberForm[x, ExponentFunction -> (If[-1 < # < 1, Null, #] &)];
format[x_] := x;
$Post = format;

When you execute these statements, the output formatting will persist for the rest of the mmka session. If you want to go back to the default output format in the session, execute

$Post = oldPost;

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"I attribute essentially all my success to the very large amount of chocolate that I consume.  Personally I feel that milk chocolate makes you stupid.Now dark chocolate is the way to go. It's one thing if you want like a medicine or chemistry Nobel Prize, OK, but if you want a physics Nobel Prize it pretty much has got to be dark chocolate."

--- Erik Cornell

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