Fock space dualities

Abstract

Several cases of Fock space duality occurring in the theory of many-body systems in general and nuclei in particular are discussed. All of them are special cases of a general duality theorem proved in mathematics by Howe in the 1970s. Dualities on a fermion Fock space between orthogonal Lie algebras and related groups, including an o-Pin duality recently discovered by the author, present a nice, symmetric pattern.

Comments: Presented at The International Workshop "Shapes and Dynamics of Atomic Nuclei: Contemporary Aspects" (SDANCA-21), 16-18 September 2021, Sofia, Bulgaria