Playing with the enveloping algebra of supersymmetry
E. Cattaruzza, E. Gozzi
TL;DR
This paper demonstrates a method to extract the first component of a scalar superfield using a similarity transformation, revealing different algebraic structures of the generators in four and one dimensions.
Contribution
It introduces a novel approach to relate superfield components to algebraic structures within supersymmetry, highlighting the role of the enveloping algebra in four dimensions.
Findings
Generators in D=4 are in the enveloping algebra of supersymmetry.
Generators in D=1 belong to the basic algebra.
Method provides a new perspective on superfield component extraction.
Abstract
In this paper we show how to obtain from a scalar superfield its first component via a similarity transformation. We prove that in D=4 the generators of this similarity transformation live in the enveloping algebra of supersymmetry while for D=1 they belong to the basic algebra.
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