Standard Model and Beyond · Problem 3.5

Gauge Theories

Physics — Particle Physics · operator-identity-bch

Problem

Prove the formal power series identity

e^A B e^{-A} = B + [A, B] + \frac{1}{2!}[A, [A, B]] + \frac{1}{3!}[A, [A, [A, B]]] + \cdots,

where

A

and

B

are any two operators or square matrices of the same dimension.