Introducci\'on a la supersimetr\'ia

TL;DR

This paper provides an elementary introduction to supersymmetric quantum mechanics, explaining core concepts and constructing a superalgebra representation using Witten's model, aimed at graduate students in mathematics.

Contribution

It offers a detailed, accessible explanation of supersymmetric quantum mechanics and demonstrates the realization of Heisenberg's superalgebra within a supervector space framework.

Findings

Constructs a realization of Heisenberg's superalgebra as a subalgebra of endomorphisms.

Uses Witten's model to illustrate supersymmetric quantum mechanics.

Provides an educational resource for graduate students in mathematics.

Abstract

These notes are an elementary introduction to supersymmetric quantum mechanics for students of mathematics. We start from the very basic concepts of quantum mechanics and proceed to construct a realization of Heisenberg's superalgebra as a subalgebra of the graded algebra of endomorphisms of a certain supervector space (obtaining thus an example of Ado's theorem for Lie superalgebras), using Witten's model of supersymmetric quantum mechanics. The notes were written for a graduate seminar at the Universidad Aut\'onoma de San Luis Potos\'i.