Reduced N=2 Quantum Mechanics: Descendants of the Kahler Geometries

TL;DR

This paper introduces a method for reducing bosonic degrees of freedom in N=2 quantum mechanics, exploring nonstandard superalgebra representations and their geometric origins.

Contribution

It presents a systematic 'dynamical reduction' technique for N=2 quantum mechanics and discusses the classification of nonstandard superalgebra representations.

Findings

Constructed representations with fewer bosonic than fermionic degrees of freedom.

Proposed a systematic reduction method called 'dynamical reduction'.

Highlighted open problems in classifying nonstandard N=2 superalgebra representations.

Abstract

We discuss an N=2 quantum mechanics with or without a central charge. A representation is constructed with the number of bosonic degrees of freedom less that one half of the fermionic degrees of freedom. We suggest a systematic method of reducing the bosonic degrees of freedom called ``dynamical reduction." Our consideration opens a problem of a general classification of nonstandard representations of N=2$ superalgebra.