Proof of Jacobi identity in generalized quantum dynamics

TL;DR

This paper proves that the Jacobi identity holds in a generalized quantum mechanics framework that includes both fermionic and bosonic fields without assuming their mutual commutativity.

Contribution

It establishes the validity of the Jacobi identity in a new generalized quantum dynamics model, extending previous formulations.

Findings

Jacobi identity is satisfied in the generalized framework

The proof applies to mixed fermionic and bosonic fields

No assumptions about mutual commutativity are needed

Abstract

We prove that the Jacobi identity for the generalized Poisson bracket is satisfied in the generalization of Heisenberg picture quantum mechanics recently proposed by one of us (SLA). The identity holds for any combination of fermionic and bosonic fields, and requires no assumptions about their mutual commutativity.