**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.Â Â In the standard literature of magnetic monopoles, there is an open puzzle:Â Can the Dirac quantization condition be obtained if gauge invariance is broken through massive photons?Â In a paperÂ I recently co-authored with Prof. Alfred Goldhaber, from Stony Brook, we answer this question in the affirmative.

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

**NEUTRON STARS**

Neutron starsÂ 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 starsÂ receive anÂ intrinsicÂ “kick”Â at birth, which originates their large space velocities.Â The research I have done in is centered on this specific problem.Â

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

**PHYSICS TODAY PAPERS**

I have published three papers in Physics Today. The first one, back when I was a High School student, is an apologia for individualism in physics.Â This essayÂ was the most viewed article of 2013 in Physics Today’s online edition. The second piece is a critical essay againstÂ the traditional physics teaching.Â The origin ofÂ this essay was an invitation from Physics Today’s editor to write it. This essay was recently named amongst the ten most popular Physics Today articles of 2017.

- R. Heras,Â Individualism: The legacy of great physicists,Â Commentary & Reviews, Physics Today Online (October 2013).Â Named the most viewed article of 2013 in Physics Todayâ€™s Online Edition.Â
- R. Heras,Â Commentary: How to teach me physics: Tradition is not always a virtue,Â Physics TodayÂ
**70**, 3, 10Â (2017) [PDF] (paper by invitation of Physics Todayâ€™s editor). Named amongst the ten most popular Physics Today articles of 2017. See, A. Grant, The most popular Physics Today articles of 2017,Â Commentary & Reviews, Phys. Today Online (December 2017). - R. Heras,Â Readers weigh in on how to teach physics, Phys. TodayÂ
**70**, 11, 11 (2017) [PDF].

**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.Â

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

**HISTORY OF RELATIVITY**

In 1887 Woldemar Voigt published the paper “On Doppler’s Principle,” in which he demanded covariance to the homogeneous wave equation in inertial reference frames, assumed the invariance of the speed of light in these frames, and obtained a set of spacetime transformations different from the Lorentz transformations. My papers on the history of relativity are centered on this subject.

- R. Heras,Â A review of Voigt’s transformations in the framework of special relativity,Â arXiv:1411.2559 [PDF].
- R. Heras,Â Â The wave equation in the birth of spacetime symmetries,Â arXiv:1407.3425 [PDF].