Exactly soluble models with an odd number of Majorana fermions

A new class of SO(3)-invariant quantum-mechanical systems, Jk, of (2k + 1) Majorana fermions is displayed. Their Fock-space description is developed. It provides, for each fixed integer k, a finite number of energy levels EJ = 12J(J + 1) of degeneracy (2J + 1). The models have several striking features. One of these is the set of allowed J-values: for k = 1,2,3,…, these are J = 12; J = 32; J = 3 and J = 0 ….