Additivity in Kramers Pairs Symmetry: Multiplets with up to Four Unpaired Electrons

摘要

Many fermions Kramers pairs formalism is considered from the prospective of the sum of individual single fermion time-reversal operators. The obtained many fermions "pseudo Kramers pairs operator" ((K) over cap'), as well as its square ((K) over cap '2), have formally the same structure as the many fermion spin operators (S) over cap and (S) over cap (2). Nevertheless, the shape of (K) over cap '2 eigenfunctions with respect to (S) over cap (2) and (S) over cap (z) is different. Herein all Kramers adapted eigenfunctions of (K) over cap '2 for cases of up to four unpaired fermions are compiled, and their properties with respect to (K) over cap' further advocated. It will be shown that degeneracy of the (K) over cap '2 multiplets recovers the proper behavior with respect to Pascal's triangle. A projection operator for obtaining the "high spin" Kramers adapted eigen-functions is suggested. Noncommutation of (K) over cap '2 with spin and angular momentum operators and degeneracy is discussed at last. (C) 2016 Wiley Periodicals, Inc.