Robert Mann - An Introduction to Particle Physics and the Standard Model · Problem 11.6.5

Quantum Electrodynamics — Robert Mann

Physics — Particle Physics · lorentz-transformation-gamma-matrices

Problem

Writing exp⁡[i2ωμνΣμν]=S\exp\left[\frac{i}{2}\omega_{\mu\nu}\Sigma^{\mu\nu}\right] = \mathcal{S}, show S−1γμS=Λ  νμγν\mathcal{S}^{-1}\gamma^\mu\mathcal{S} = \Lambda^\mu_{\;\nu}\gamma^\nu where x′μ=Λ  νμxνx^{\prime\mu} = \Lambda^\mu_{\;\nu}x^\nu is a Lorentz-transformation. (Hint: use exp⁡(z)=lim⁡N→∞(1+zN)N\exp(z) = \lim_{N\to\infty}\left(1 + \frac{z}{N}\right)^N.)

Related theory

Browse the problem library