---
date: 2022-02-13 16:10
modification date: Sunday 13th February 2022 16:10:00
title: superalgebra
aliases: [superalgebra, Heisenberg algebra, supersymmetry, supersymmetric]

---

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# superalgebra

![](attachments/Pasted%20image%2020220213164044.png)

![](attachments/Pasted%20image%2020220213161003.png)

# Supersymmetric algebras

![](attachments/Pasted%20image%2020220213161320.png)

- The $\mathcal{N}=1$ supersymmetry algebra in $0+1$ dimensions is the **de Rham algebra**, which consists of
	- the exterior derivative $d$ 
	- its adjoint $d^{\dagger}$ with respect to the inner product $\inp{a}{b} = \int_M \hodgestar a \wedge b$, 
	- their anticommutator, 
	- the [Laplacian](Laplacian.md), which is the [Hamiltonian](Hamiltonian.md) operator of the theory, and commutes with the supercharges).

![](attachments/Pasted%20image%2020220213223539.png)