Abstract
Symmetries in neutrino physics are explored using analogies to fermion pairing in many-body systems. In particular, the SO(5) symmetry of the most general neutrino mass Hamiltonian with both Dirac and Majorana mass terms as well as the invariants of certain limits of the collective neutrino Hamiltonian are discussed. The latter Hamiltonian finds applications in the Early Universe and core-collapse supernovae.
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