## A day as a physicist

I speak often in my blog about technical matters as I believe these represent the most important part of my intellectual activity. Indeed, my work is so extended in so much areas of physics due to the fact that I am largely involved about problematics of theoretical physics. So, I would like to tell you about my main activities today as a physicist. In these days I am involved in a collaboration with Marco Ruggieri (see here). Marco is working on the understanding on how QCD vacuum gets modified by strong magnetic fields. This question is relevant as such physical effects could be observed at LHC and so, having a prevision for them is paramount. Hurdles here arise from the fact that we currently miss a low-energy full understanding of QCD and one is forced to use phenomenological models that are more or less useful in this case. Typical choices are Nambu-Jona-Lasinio model and the $\sigma$ model with a pion field coupled. In this way one can arrange some theoretical previsions about magnetic susceptibility and other observables. Strange as may seem, these two models can be made to coincide and so, what one can predict with Nambu-Jona-Lasinio model is there also with the  $\sigma$ model.

The reason why these two largely known models can coincide arise with bosonization techniques (see here). If you start with a linear $\sigma$ model assuming just a mass term and you consider its interaction with a fermion field (Yukawa model), you can integrate away the fermion field. This integration will make the potential of the scalar field absolutely not trivial and the vacuum is no more the standard 0 but you will get a mass gap equation. The old Yukawa model gives a really non trivial physics and chiral symmetry is broken. Now, one can takes the Nambu-jona-Lasinio model and, using a transformation taken from condensed matter physics (Hubbard-Stratonovich transformation), one can change a quartic fermion interaction into a quadratic scalar term with a scalar and a pseudoscalar field (the pion) interacting with the quark fields, the same terms taken into the $\sigma$ model. At this stage one can generate a mass gap equation, the one well-known in literature and the same that can be obtained form the $\sigma$ model. One can make the two models identical at this order. Now, going to higher orders, loop expansion produces kinematic terms in the Nambu-Jona-Lasinio model and higher order corrections to the potential of the  $\sigma$ model. I would like to check these higher order corrections between the two models. But one can see that the Yukawa model can be reduced to a contact interaction between fermions as I have proved quite recently (see here). So, there is a deep relation betwenn the Nambu-Jona-Lasinio model and the Yukawa model. I would like to prove a theorem about but, for the moment, this is just an on-going work with Marco.

Finally, a beautiful way a physicist has to contribute to our community is acting as a referee for journals. I am doing this work since 1996 when American Physical Society hired me through the good help of an associate editor of Physical Review A. This is an important way to help science as progress is achieved through the cooperation of several people in the community and if today we see such a great understanding of the World around us is just because such a cooperation worked satisfactorily well. Indeed, this is a honor for a scientist.

Last but not least, I like to write as I am doing now to let things widely known. This is what I hope I am doing better.

D. Ebert (1997). Bosonization in Particle Physics arxiv arXiv: hep-ph/9710511v1

Marco Frasca (2010). Glueball spectrum and hadronic processes in low-energy QCD Nucl.Phys.Proc.Suppl.207-208:196-199,2010 arXiv: 1007.4479v2