Deriving the Dirac Equation

Hey all, thanks for checking out this video! :) While reviewing the video just now, I realized I probably should have been more clear about covariance and contravariance. This affects the sign of the momentum terms (more generally, the space-like terms), and is a perennial source of dropped minus signs 😅 The plus signs at 13:20 are due to using the contravariant Dirac matrices, three of which which absorb the minus signs, see the Wikipedia article “gamma matrices” for more info. Anyway, the main idea I hope you’ll take away from this video is that the anticommutation relations for the Dirac matrices arise from taking the square root of the mass shell

Dirac was known for both the brevity and precision of his speech. At a conference he was lecturing and writing at a blackboard. A member of the audience said at the conclusion of Dirac's presentation, "I don't understand your equation in the upper right." Dirac said nothing and returned to his seat at the table with other lecturers. After an uncomfortable silence, the conference moderator asked, "Mr. Dirac, are you going to answer the man's question?" Dirac: "It wasn't a question. It was a statement."

The "I'm letting the squares breathe..." was genius for geometrically visualizing variables!

A thousand jargon-filled wikipedia articles could not have given me the clarity I now posess thanks to this video. Thanks so much

This sort of accessible education will prove to be revolutionary.

Fun fact. Back in 1972 I was taught some mathematical physics by the late Joe Moyal. Joe was invited by Dirac to Cambridge during the World War 2 to discuss Joe's work on statistical foundatiions of quantim mechanics (there is a 1947 paper with Bartlett and Kendall which also deals with the issues). Joe met Dirac and I can say that I have shaken hands with someone who has shaken hands with Dirac.

When the math is shouting “PARTICLES AREN’T FUNDAMENTAL, THEY’RE EMERGENT, YOU’RE JUST DOING EPICYCLES AGAIN”

Straight-up the best physics videos on youtube

The teacher I had for QFT was one of the best teachers i ever met, and yet, this is so much more insightful then what he ever managed on a blackboard. The visualisation is genius.

The reason the coefficients don't commute (so the opposite breathing squares cancel out) and why the coefficient squared are negative numbers, is because a spinor is a unit quaternion! In fact, the nature of spin is a bit less mysterious if instead of using Dirac matrices we use quaternions, for rotations on a 4D hypersurface :)

It's also worth noting that the matrix approach is entirely equivalent, mathematically, to the other ways. It's not just that matrices happen to solve this particular problem - matrices form a group, and that group is isomorphic with any group that obeys the same multiplication rules. So not only is this "a way to do it" - you also don't lose ANYTHING by doing it this way.

Wow this lesson is much better than in Oxford or Harvard. Very interesting to see visualisation of solution of Dirac equation to compare with Klein-Gordon and Schrodinger equations. Also very interesting to see how do the wave functions in the bispinor responsible for spin up, spin down, and antimatter affect each other

I never heard of this way of deriving the equation and now the matrices seem so much more understandable... Congrats dude, you just did the impossible of explaining all of this stuff I tried to understand for months

eigenchris's "Spinors for Beginners" series is a really good introduction to, well, spinors for beginners!

Absolutely terrific :) btw, here's a tip for everyone who sees this: geometric (Clifford) algebra really helps understanding these spinors better (and also space-time in general).

Wow. I have devoted all of my time to getting into GR and have only had a basic rundown of QM but have wanted to get into the more interesting QM stuff for a while. You did a great job and I love hearing your excitement for introducing new ideas. That was perfect and felt so clean. Great stuff!!!!

I know the Dirac equation but never really saw it being derived before. Either I was incredibly blind in my education or my educators hand waved everything and I struggled from there. These videos are opening my eyes more than my entire journey through undergrad and honors.

I recently started my postgraduate physics studies and one of my modules (which is by far the hardest one for me) covers the Klein-Gordon equation and (now) Dirac equation. The reading material and textbooks for most of the part pretty much assumed the reader knows how to derive certain things and/or where it comes it or what it represents etc, which is why I'm finding them incredibly difficult. Your videos have literally saved my life by providing the much needed intuition for these topics. Keep up the amazing work!

I think this is the clearest picture of Dirac equation and I have minimal training in math and physics 😊

I was watching Alexander Fufaev video on the Schrodinger equation (He gave an excellent explanation), and he mentioned Diracs equation as the next thing for relativistic SE. I'm happy to have found this. It's been years since I finished. So here I am learning new things and brushing up the old, to enable drawing out something new if I persist just enough. This is excellent and widened my understanding but raised further questions too.