Generalized Coherent States for Dynamical Superalgebras

TL;DR

This paper extends the concept of coherent states to general Lie superalgebras, exploring their algebraic and geometric properties, including Kähler structures and connections to coadjoint orbits, with applications to specific superalgebras.

Contribution

It introduces a method to define coherent states for Lie superalgebras and analyzes their geometric structures, advancing the understanding of superalgebra representations.

Findings

Defined coherent states for Lie superalgebras using Perelomov's method

Analyzed algebraic and geometric properties of these states

Connected supermanifold structures to coadjoint orbits

Abstract

Coherent states for a general Lie superalgebra are defined following the method originally proposed by Perelomov. Algebraic and geometrical properties of the systems of states thus obtained are examined, with particular attention to the possibility of defining a K\"ahler structure over the states supermanifold and to the connection between this supermanifold and the coadjoint orbits of the dynamical supergroup. The theory is then applied to some compact forms of contragradient Lie superalgebras.