# Note on the super-extended Moyal formalism and its BBGKY hierarchy

## TL;DR

This paper extends the Moyal formalism for quantum mechanics by incorporating higher differential forms and Grassmann variables, deriving a super-extended BBGKY hierarchy through functional methods.

## Contribution

It introduces a super-extended Moyal formalism with Grassmann variables and derives the associated BBGKY hierarchy using functional integral techniques.

## Key findings

- Extended Moyal formalism with Grassmann variables
- Derivation of super-extended BBGKY hierarchy
- Distribution functions depend on Grassmann odd fields

## Abstract

We consider the path integral associated to the Moyal formalism for quantum mechanics extended to contain higher differential forms by means of Grassmann odd fields. After revisiting some properties of the functional integral associated to the (super-extended) Moyal formalism, we give a convenient functional derivation of the BBGKY hierarchy in this framework. In this case the distribution functions depend also on the Grassmann odd fields.