Deriving The Dirac Equation 

At 3:18 you said that g_{\mu u} p^{ u} = 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

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

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

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

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!

Me, currently doing Physics 1 classical Mechanics and Calculus II: What the fuckshit mickey mouse is this What the shitfuck daffy duck is that

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!!!

This was great! Thank you so much for making this! It was fun to watch and you are a great talker/teacher. I loved just listening to you talk and not needing to regurgitate it next week for an exam lol. I find many of my professors try to skip stuff and don't always write out all the smaller steps involved in these kinds of proofs. It was greatly appreciated that you lengthened your video and took the time to write everything out! Keep up the great work man!

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

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

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!

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

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!

Derive the standard model lagrangian next please!

Man allergy season this year is crazy you were sneezing all video, bless your soul.

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

one of your best videos! nicely done!

thank you each time for your persistence

Sweet! Concise and clear, dude you’re the best!

Ive been watching a lot of these series lately. I watched both susskind series on gr and various diff geom series but i think ive made a lot more conceptual connections with this series. Muchas gracias

Thanks for video! This video is a common textbook derivation but there is a better first principals approach that is more correct and provides deeper insight. Quantum wave functions are representations for rotational symmetry in space-time; the simplest representation is a scalar, the next simplest is a spinor (spin 1/2), next is the vector (spin 1), etc. Spinors are the building blocks used to make vectors, tensors and other higher order symmetry representations. The chiral spinors (Weyl spinors) are contraspinors (right-handed spinors) or cospinors (left-handed) spinors; contraspinors make contravariant vectors and cospinors make covariant vectors. Parity means invert the spatial components of a vector; this corresponds to switching right-handed and left-handed spinors (right->left and left->right). A single chiral spinor generates a vector (momentum) and pseudovector (spin); the momentum represents a particle with no mass and the representation is not parity invariant. Use both chiral spinors (bispinor or Dirac spinor) and it is possible to generate a vector (momentum) representing a particle with mass and a representation that is parity invariant. This is a correct representation for an electron. Steane (see reference) uses these principals to generate the correct spinors and uses simple algebra to transform this solution to the Dirac equation. Sperança (see reference) generates a Dirac operator from the Dirac equation and shows that the Dirac operator is actually a parity operator; solving the DIrac equation means finding the spinors needed for parity invariance. References: Llohann D. Sperança. International Journal of Modern Physics D, 2018; An introduction to spinors, Andrew Steane, 2013, arxiv.org/abs/1312.3824.

This was simply awesome. Thanks for making this.

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!!!

Thanks for making this video Andrew!

i've just finished watching your video, and it was just amazing, thank you!!

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.

wow. Thank you very much. I was reading this from David Tong QFT lecture notes and I was little confused. But this video made it crystal clear.

Definitely enjoyed this derivation video. Looking forward to its Interpretation!

Thanks a lot Mr.Dotson. Was in real need of this.

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

Exactly what I needed for my Introduction to particle physics course. Thank you :)))

This was really cool to watch and I think I actually understood most of it for once. Glad to have this famous equation finally make a little sense.

I struck gold today. Fantastic channel. Just subscribed. Keep this very interesting lectures coming they are quite useful. I second a suggestion below that the Dotson should be made a unit, but rather a unit of usefulness of a video on RU-vid 😁 Thanks again.

I understood more than I thought I would. Great job :)

An extremely clear presentation.

I have no idea what most of these means, but sitting through the video to see the derivation and after all that approached at an elegant equation feels fking satisfying.

I don't know why I'm watching this at 1am, but it's definitely worth it! xD (Also, since i watched this at 1am and understood it, it means you explain things really well. So thanks, and good job! 😁)

Good work ! Nice derivation with good amplification of some steps for those who have not seen it before. At the end you might have put the spinor indices back in and explained how they work, as this is a point of confusion for the novice. Oh .. and credited Feynman for his 'slash' notation.

Big thanks for making math avaliable and fun! ❤

and suddenly, many years too late, that class on particle physics makes a whole lot more sense.

Great video and such a simple derivation it seems. Why didn't I think of it? Well, this just proves the quality of your explanation! ;-)

“Dirac and roll” don’t think I didn’t catch that.

Can't wait to Dirac n roll when i actually understand this better💃💃 great video, Andrew!!

I love hardcore physics videos! Thank you for making them!

Man, you're an awesome teacher!

Excellent presentation. Only 1 typo at the anti-commutator relation for u v. Would have been nice to discuss the solutions. Great stuff.

The constant need for physicists to use shorthand notation can be so frustrating! There's already enough to memorize without having to remember what ALL of the shorthand notation stands for. LMAO. Anyway... AWESOME video! It cleared up a lot of things for me!

Dr. Dotson's teaching days of his youth. - 2019 colorized.

U make Four vector algebra look easy. Grateful☺️

Nice video... good refresher!

Great explanation.

I fully understood it. It's wonderful for me

Phenomenal Job!

absolute ripper great video by sir andrew dotson

thanks for giving such knowledge

Really elegant in 20 minutes.

Hey Andrew, I love this video! Do you think you can make the video you mentioned at the end about interpreting the Dirac equation? Would love to see how we can get antimatter from this

The only words I understood was dot product and vector, so I’m basically a fake grad student 😂

If you have a formal math training your videos are much more understandable than other phys youtubers that hide the technicalities under the rag (i.e. ty mate really nice video)

so cool. keep up the good work!!!!

That was extremely helpful, thanks

Man this is an awesome video ❤❤🙏🏼 the best 👌🏽

such a brilliant vid!

Nice presentation.

Your videos are amazing

Keep it up Andrew, the physics majors at the University of Cambridge love your content

That's legendary!! 🤘

Anyone who is interested in the Gamma matrices, read about Clifford Algebras

Oh baby, you left me way back there ....and your still going strong. As flammy would say , WTF ! It seems that your physics vocabulary has gone into the twilight's zone mode. Your education on said subject matter seems to have gone into warp speed and you have gone where you belong....... I haven't heard anyone talk in equation code for a long time. You have stepped up unto your plane of natural existence of being electrified into an extremist of sorts of a real Mr. Physics man . See you when we get to the other side of the universe. With your high knowledge you will definitely get there and back by the time that I begin. Your so speedy fast .

Great job my cousin!!

Damm i got a lot to look forward to in my physics career

Physics is always a enjoying thing to watch

I basically understood most of it, I haven't done any work in tensors or four vectors before but I don't think it's much more complex than the 3 dimensional real space. I only have my undergraduate physics degree and so we didn't get Into the Dirac equation to much. Cool video by the way

I suspect Mr Dotson is a magnificent maths tutor because I found all of his explanation utterly fascinating whilst understanding none of it whatsoever . . . .

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

Anyone else not know enough math

I'm currently in ist year of my college and didn't even got a word but still enjoyed the whole video ♥️😍

I wanna see you derive the Maxwell equations!

It's amazing man !

Him: hello smart people Everyone else: not really

I like how I have no clue what youre saying, then I take a certain class and im like, oh what andrew is talking about isnt that bad. Cant wait to go Relativity. Just finished 1st semester quantum mechanics and classical and EM. Do more EM videos cause I honeslty didnt get it the first time around.

@15:48 matrices appeal to our senses as generalizations of ordinary numbers. The fact that the cross terms, which rep interference, go to zero is counter intuitive. On the outside, this leads to the idea of spinors not being covariant objects. All the algebra aside, these core ideas are very intriguing.

At 10:30, you substituted alpha with gamma. Now gamma can only be equal to alpha for the same indices yet after your substitution they have different indices. This part irked me a bit, but yes it was very fun to watch. Great content man, and I love your style/

You are a genius. Genius

Hey man awesome content!

Boutta do a sleep but I caught this boi 5 minutes after upload. Hecc.

I have my final theoretical physics exam for my masters in a few days and this video helps me see the dirac equation from a different angle, thanks for the good video.

Great job keep it up

Yo. Your curly brackets. You came from both ways. I'm weirdly impressed

Do in the next video a derivation of the Einstein field equations from the expected value equations in economics.

At 15:25 I believe you meant to put the not equals between mu and nu (even though what you wrote turns out to be true). Anywho thanks for the great video! This makes much more sense than when my lecturer explained it

Next year when I get into uni, probably I'll understand your videos.

University of Bristol loving your content!!

I am thinking of a geometric interpretation of the Dirac equation, not sure whether it is right or wrong. Let first talk about some basic ideas of some terminology in math. Consider a space-time M (a manifold, with riemannian metric g on TM). Further consider a copy of a finite dim'l space S on each point of M (we denote the resulting space E), with projection p from E 一>M. We call the entire structure a fiber bundle p: E一>M over M with fiber S. A fiber bundle p: E一>M is of "principal" if S is a Lie group act on M( here, the Lie group is called the structure group). Consider a fiber bundle p:E一>M , with group G acts on the entire bundles, we denote the fiber bundle as an associated fiber bundle associated to a principal bundle where the fiber S is G . Interpretation: Consider the spinor bundle p:E一>M(each point of M is attached to something called a spin space, i.e. the space that characterize the spin of particles) over a space-time M, with maps Psi : M 一> E call the section of the spinor bundle. (Psi is mentioned in the video,it is also a 4-vector in space-time and its fiber spin-space)The derivatives operator is a connection tell you how Psi changes in the tangent space of space-time, and the gamma matrices tells you how the vector psi changes in spin-space (gamma matrices are rotation matrix in spin-space). the combination of the two tell you how the spin and the vector components in space-time of psi changes. It is just a guess... Apologize if I get something wrong. I am just an undergrad student.

Slash notation, what kind of wizardry is this ? In all seriousness, i liked it how you derived the Dirac Equation.

Hi there, I really liked this approach towards the derivation. Might I suggest an alternative approach where you arrive at the same set of equation starting from the decomposition of Lorentz group into two commutating SU(2) groups? I find that very elegant.

You lost me at 0:47

please do more about the dirac equation

oh yeah i have been waiting so long

As an interested learner of physics, I decided to search for a vid on deriving the Dirac Equation. Of course, my dude Andrew Dotson has a derivation vid. Boom!