Invited by Joint TDLI-SPA Lecture, Prof. Shao-Feng Ge, T. D. Lee Fellow of Tsung-Dao Lee Institute (TDLI), gave two lectures on Majorana Fermions on May 26th and June 2nd. In total about 100 audiences attended the lectures on-site or via zoom online, followed by up to 3 hours of lively discussions for each lecture.

Majorana fermion is of common interest in both particle and condensed matter physics. In particle physics the Majorana neutrino is an indication of lepton number violation and hence matter-antimatter asymmetry in the Universe while it is treasured as Angel Particle in condensed matter. However, Majorana fermion always seems not as transparent as Dirac fermion. For example, contrary to the naive expectation that Majorana neutrino is its own antiparticle, neutrino is different from antineutrino even if they are Majorana fermions. These lectures clarified these fundamental issues and introduced the rich phenomenological consequences.

There were two lectures and below is a brief introduction:

Lecture 1 (May/26): What is Majorana Fermion?

• What is spin? Angular momentum comes from space rotation while spin comes from space-time rotation
• Two-component theory & parity violation. The Lorentz group is divided into two spin groups: SU(2)_L x SU(2)_R . Correspondingly, the fermion spin is divided into left-handed and right-handed components. Parity violation means that the left-handed and right-handed fermions have different properties.
• Dirac vs Majorana fermions. The Majorana fermion is its own charge conjugate, but not its own antiparticle.

Lecture 2 (Jun/2): Majorana neutrinos

• Neutrino mixing & oscillation. Neutrino oscillation is a coherent interference effect of quantum mechanics, which comes from non-degenerate mass eigenvalues and nontrivial mixing matrix.
• Neutrino-antineutrino oscillation. If neutrinos are Majorana fermions, it is possible to have neutrino-antineutrino oscillation.
• Matter-antimatter asymmetry & Leptogenesis. There is a large amount of matter in the universe, but there is almost no antimatter. The Dirac CP phase and the Majorana CP phases in the neutrino mixture can explain the existence of matter through the leptogenesis mechanism.
• Neutrinoless double beta decay: This process is equivalent to two beta decays, but with two electrons and no neutrinos in the final state. Instead, the neutrinos appear as virtual particles in the intermediate state. This decay process  can test whether neutrinos are Majorana fermions.
• Cosmic neutrino background: A large number of neutrinos were produced in the early universe and this relics can be measured by the scattering of neutrinos with tritium nuclei.
  
  

These two lectures were mainly intended for undergraduates, graduate students and postdoctoral researchers in quantum and particle physics. In addition, a number of fellows joined and contributed a warm exchange and discussion. The lecture slides and videos can be accessed via the following link:  https://indico-tdli.sjtu.edu.cn/event/189/