Noether's Theorem and the Momentum of the Klein-Gordon Field

In this video I will prove noether's theorem and use it to derive equation 2.18 and 2.19 from peskin and schroeder's QFT book. We will find the conserved charges associated to the Klein-Gordon field under spacetime translation, which will turn out to be the energy and momentum of the field! If you enjoy my content, please consider checking out my Patreon! www.patreon.com/nickheumann Also, consider subscribing and following me on my socials! twitter: twitter.com/nickheumann Instagram: instagram.com/nicolasheumann twitch: www.twitch.tv/nickheumann My name is Nick Heumann, I am a recently graduated physicist. I love to teach physics, so I decided to give YouTube a try. English is not my first language, but I hope that you can understand me well enough regardless. ▬ Contents of this video ▬▬▬▬▬▬▬▬▬▬ 00:00 Introducing the necessity for studying symmetries 00:45 What is a symmetry? 01:45 Introducing Noether's Theorem (conserved currents) 02:57 Proving Noether's Theorem 12:00 Introducing Noether's Theorem (Conserved Charges) 12:54 Proving it 15:10 Example - Finding the Energy-Momentum Tensor for Klein-Gordon field 27:30 Please consider supporting me on my patreon!