ar X iv : h ep - t h / 06 10 22 8 v 1 2 0 O ct 2 00 6 Homage to Ettore Majorana ∗

I am privileged to be in this interesting place honoring Ettore Majorana. Of course I have had no personal contact with him — he disappeared before I appeared. However, it is surprising, that I did not encounter his name nor his achievements during my physics education. He is hardly mentioned in the usual textbooks, at least in the American ones. This is a great loss! To me it was a special loss for the following reason. When I was preparing with Hans Bethe our quantum mechanics textbook, I became fascinated by the Thomas-Fermi theory, and I strived to give a complete discussion in our text. But at that time I knew nothing about Majorana’s work in this area, and so could not include it. Again, when we were writing the chapters on Dirac theory, I wondered why only charged fermions are considered. The resolution of my puzzlement lay in the Majorana representation, about which I learned only later, principally through Julian Schwinger’s writings. Schwinger apparently appreciated the Majorana approach and in his discussions of Dirac theory, the charge carrying fermion field is usually presented as the complex superposition of two real fields, in complete analogy to the description of charged boson fields. Another connection between Majorana and Schwinger can be noted. The last topic that Schwinger researched concerned corrections to the Thomas-Fermi model. Schwinger was also interested in the problem of mass generation, a topic which these days is linked to Majorana’s name. I shall use this point of contact between the two scientists to review Schwinger’s mass generation mechanism [1], to expose its topological underpinings and to present an interesting generalization [2]. Majorana deconstructed the complex Dirac equation into its real components. Here I deconstruct Schwinger’s mass generation into its topological ingredients. I think that Majorana would have liked these results.