Deriving The Dirac Equation

Today I derive the famous Dirac equation. I talk about four-vector notation and contraction, as well as laying out the requirements for the anticommutator relation of gamma matrices.

Dot products of four vectors:

Deriving the Klein Gordon Equation:

[ShaunRL]

At 3:18 you said that g_{\mu \nu} p^{\nu} = g_{00} p_{0} + g_{11} p_{1 }+ ... when it should be a four vector (g_{00} p_{0}, g_{11} p_{1 }, ...) not a sum

[bryamayvar]

level 1 tensor boi tries to understand level 7 tensoir boi gone wrong xd

[anuj]

Dirac says "Okay" from heaven.
He is a man of few words.

[SuperMariocapo]

Even though I didn't understand a thing about this, I still watched the video because you explain everything in such a good way that you make it seem simple maths!

[McRaylie]

Can we make the Dotson an actual unit, like how a Smoot is a unit.

[glfouym]

Whenever I'm really desperate to drive a part of the equation somehow magically this channel have a video about it so thank you i wish your thesis going well.

[sahhaf]

You definitely have to do this "interpretation of dirac equation" video and show us how spin naturally comes out as a consequence of dirac equation!!!

[anubhavdec]

I had loads of fun man. I might sound embarrassing but I'm gonna say it. When you finally arrived at the equation, I had goosebumps!

[fabiansepulveda]

Finally someone can explain this in a simple way! Thanks for all of your videos Andrew!

[dcterr]

Very good explanation! I like how you avoided using the alpha and beta matrices, which is the usual way I've seen it derived.

[samvelasco]

Me, currently doing Physics 1 classical Mechanics and Calculus II:


What the fuckshit mickey mouse is this
What the shitfuck daffy duck is that

[nitrozox]

Derive the standard model lagrangian next please!

[Cloclo]

That was great! I had missed the day when my professor had derived this in my particle physics class, but this clarifies a lot. I salute you sir

[joshyman]

Excellent video, I’m fairly comfortable with 4 vectors after having done my general relativity course where I got used to thinking as space time as a pseudoriemannian manifold. However, I hadn’t seen this gamma vector (with matrix components) or seen how one applies ideas of QM in here and I found the way you explained these to be very clear and easy to follow. Thanks!

[seanpaul]

I was learning quantum field theory but was having a hard time wraping my head around Dirac equation this video helped a lot keep up the good work

[Fflurie]

"What's up smart people" Heheh, bold of you to assume that I'm smart

[ronaldjorgensen]

thank you each time for your persistence

[syedmraza]

Looked at this video a year ago, didnt understand much, but last winter break i read a book on tensor calculus and recently got into quantum computing and had to do some clifford algebra, now this makes complete sense!!!

[ShubhamBhushanCC]

I have a master's degree in Physics from one of the finest Universities in my country and none of my professors ever, I repeat ever derived Dirac equation. They just handwaved over it. Fucking hate that. Thank you for doing this

[robertschlesinger]

Excellent video on the Dirac Equation. Paul A.M. Dirac was a great genius, and like many high functioning geniuses, was rather eccentric. A couple of credible anecdotes follow:

A French physicist came to Dirac's home to discuss some cutting edge physics.   The physicist was escorted into Dirac's study and he preceded for some time, trying with great difficulty to explain his work in English to Dirac.   The physicist was clearly having considerable frustration with his limited spoken English.   After quite some time, Dirac's sister, Betty, entered the study with some tea and biscuits, speaking fluent French, and wherein Dirac responded in fluent French.  The French physicist who had spent considerable time frustrated in trying to express himself in English inquired of Dirac: Why didn't you tell me you spoke French.   Dirac replied: You didn't ask.

Another anecdote is from his days at Florida State University.     The Physics Department held seminars which Dirac would often attend, sitting near the front row.  He appeared to be dozing off throughout the presentations, but during the question & answer period, he would make brilliant comments and ask appropriate questions.   He seemed asleep, but was all the while quite lucid.