Thursdays at 3:00 pm in Research Hall room 163
Jentschura abstract: In 1943, Wolfgang Pauli wrote an article for the Reviews of Modern Physics in which he argued that the Hermiticity requirement for quantum mechanical Hamiltonians can be relaxed and generalized to a weaker requirement, that of so-called pseudo-Hermiticity. All of the concepts introduced by Pauli into theoretical physics have found deep and far-reaching applications — except this one, up and until recently. Using pseudo-Hermiticity, or PT symmetry, it has been possible not only to solve a number of fundamental problems in mathematical physics, but also, to describe quite interesting quantum optical phenomena in a concise and transparent formulation. This talk will be focused on pseudo-Hermitian generalizations of the Dirac equation, which is a first-order differential equation acting on four-dimensional spinor space. A theory of the neutrino based on a generalized Dirac equation has a number of desirable properties: it suppresses the right-handed neutrino, and left-handed anti-neutrino state due to negative norm, conserves the concept of lepton number, and allows for plane traveling-wave solutions. By contrast, a Majorana neutrino would force us to abandon the concept of lepton number altogether, and the Majorana equation does not allow for traveling-wave solutions in first quantization. The emergence of massive neutrinos forces us to re-think basic concepts of the standard model, which originally called for massless (Weyl) neutrinos. The theoretical description of a massive neutrino provides for much greater challenges
than a massless neutrino.