Uploads from eigenchris

Currently Playing: Spinors for Beginners 24: Proca and Maxwell Equations (derivation + solutions)

Full spinors playlist: https://www.youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBs Leave me a tip: https://ko-fi.com/eigenchris Powerpoint slide files + Exercise answers: https://github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginners My videos on gravitational waves: https://www.youtube.com/watch?v=ofi9VllCOxI&list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQa&index=34 0:00 - Rewriting Maxwell Equations 5:02 - Maxwell Lagrangian 8:06 - Proca Lagrangian + Lorenz Condition 10:44 - Solving for vector amplitudes 17:19 - Three Polarizations 21:39 - Maxwell Solutions 24:25 - What is a Gauge Transformation? 26:37 - Gauge transforming Lagrangians 28:06 - No Maxwell Longitudinal Polarization 32:13 - Complex Proca + Anti-particles