Monthly Archives: May 2013

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

\mathcal{L}^{\prime}=g~\phi\bar{\psi}\psi,


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

 H_{D} =c\mathbf{\alpha\cdot p}+\beta m_{e}c^{2}+V^{\prime}.

(I suppress interactions of electrons with each other and with the nucleus). Given \mathcal{L}^{\prime} what is that extra operator V^{\prime} that I would have to add to my Dirac Hamiltonian? I consistently derive V^{\prime} 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).

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.