**MAGNETIC MONOPOLES**

I became interested in magnetic monopoles last year. The aesthetic nature of the symmetrized Maxwell’s equations is what initially drove me to the subject and I have been fairly fascinated towards it ever since.

In the standard literature of magnetic monopoles, there is an open puzzle: Can the Dirac quantization condition be obtained if photons have a finite mass? It is commonly believed that magnetic monopoles and massive photons are two incompatible ideas because one cannot derive the Dirac quantization condition. However, in a paper I recently co-authored with Prof. Alfred Goldhaber, from Stony Brook, we answer this question in the affirmative.

- A. S. Goldhaber & R. Heras, 2017, Dirac Quantization Condition Holds with Nonzero Photon Mass, arXiv:1710.03321 [PDF].

**NEUTRON STARS**

Neutron stars are the extremely dense remnants of massive stars after they die and explode as supernovae. These amazing compact remnants have the strongest magnetic fields in the universe, super high densities, and very high velocities. What initially drove me to this subject back in high school is the fact that no one has come up with a concise explanation as to why neutron stars receive an intrinsic “kick” at birth, which originates their large space velocities. The research I have done in is centered on this specific problem.

- R. Heras, 2016, Magnetorotational instabilities and pulsar kick velocities, N Astron.
**43**, 6 [PDF] - R. Heras, 2013, Birth accelerations of neutron stars, Proc. IAU., S.
**291**, 399 [PDF]. - R. Heras, 2012, Pulsars are Born as Magnetars, ASP Conf. Ser.
**466**, 253 [PDF]. - R. Heras, 2011, The magnetar origin of pulsars, arXiv:1104.5060 [PDF].
- R. Heras, 2011, Initial accelerations of pulsars caused by external kicks, arXiv:1103.1929 [PDF].

**PHYSICS TODAY PAPERS**

I have written three opinion pieces in Physics Today! The first one, back when I was in high school, is an apologia to individualism in physics: “Individualism: the legacy of great physicists.” The second paper is a critique of physics education, written in the form of an essay entitled “How to teach me physics: tradition is not always a virtue.” This was a paper by invitation of Physics Today’s editor. Three professors made comments on this paper and I was invited to reply.

- R. Heras, Readers weigh in on how to teach physics, Phys. Today
**70**, 11, 11 [PDF]. - R. Heras, 2017, Commentary: How to teach me physics: Tradition is not always a virtue, Physics Today
**70**, 3, 10 [PDF] (invited paper). - R. Heras, 2013, Individualism: The legacy of great physicists, Commentary & Reviews, Physics Today Online (October). Named the most viewed article of 2013 in Physics Today’s Online Edition. See related comment in Scientific American.

**TEACHING: RELATIVITY AND ELECTRODYNAMICS**

I have not much to add in this section, but to say that relativity and electrodynamics are two of my most loved topics in physics. I take a great amount of pleasure in studying the details of these theories as well as teaching them every time I got the chance.

- R. Heras, 2017, Alternative routes to the retarded potentials, Eur. J. Phys.
**38**055203 [PDF]. - R. Heras, 2017, Four easy routes to the Lorentz transformations: addendum to ‘Lorentz transformations and the wave equation,’ Eur. J. Phys.
**38**, 019401 - R. Heras, 2016, The Helmholtz theorem and retarded fields, Eur. J. Phys,
**37****,**065204 [PDF] - R. Heras, 2016, Lorentz transformations and the wave equation, Eur. J. Phys.
**37,**025603 [PDF].

**HISTORY OF RELATIVITY**

It turns out that in 1887 an unknown physicist named W. Voigt almost (without realizing it) discovered special relativity! He derived a set of space-time transfomrations now known as Voigt transformations by demanding covariance of the wave equation. I got interested on his seminal paper and decided to studied it. My paper on the history of relativity deals with Voigt’s seminal work.

- R. Heras, 2014, Voigt’s transformations in the beginning of the relativistic era, arXiv:1411.2559 [PDF]
- R. Heras, 2014, The wave equation in the birth of spacetime symmetries, arXiv:1407.3425 [PDF].