TL;DR
This paper discusses various instances of Fock space duality in many-body physics, highlighting a unifying mathematical theorem and exploring dualities involving orthogonal Lie algebras, including a recent o-Pin duality discovery.
Contribution
It unifies different Fock space dualities under Howe's general theorem and introduces a new o-Pin duality involving orthogonal Lie algebras.
Findings
Multiple cases of Fock space duality are explained as special instances of Howe's theorem.
A new o-Pin duality involving orthogonal Lie algebras is presented.
The dualities exhibit a symmetric pattern across different physical systems.
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.
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