Sidney Coleman — Quantum Field Theory Lectures · Problem 1.1

September 23 - Units; Translational invariance, Rotational invariance and Lorentz invariance for a single free particle — Sidney Coleman

Physics — QFT · rotational-invariance-single-particle

Problem

Prove that

U(R)^\dagger H U(R) = H

(equation (1.8)), where

U(R)|\vec{k}\rangle = |R\vec{k}\rangle

and

H|\vec{k}\rangle = \omega_{\vec{k}}|\vec{k}\rangle = \sqrt{|\vec{k}|^2 + \mu^2}|\vec{k}\rangle