Deriving The Dirac Equation
ฝัง
- เผยแพร่เมื่อ 4 มี.ค. 2019
- 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:
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Deriving the Klein Gordon Equation:
• Deriving The Klein Gor... - บันเทิง
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
You're right. I was trying to hit home that only the mu=nu terms survive, attached to their basis vectors, but writing it as the sum was not correct. Thanks for the catch!
Instead of using the "Dotson" you can just do 1 lightsecond/second
ShaunRL Yes I totally understood that
forgive my extreme math stupidity but where do you get e2-p2-m2 is zero?
@@16rumpole Rewriting einstein's energy mass equivalence principle but with c=1
level 1 tensor boi tries to understand level 7 tensoir boi gone wrong xd
I am a Level 0. I understand absolutely nothing but enjoy looking at algebra.
Andrew is now level ∞ tensor boi now
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.
Dirac was very sure that he was NOT going to heaven.
Kvothe o Sem-Sangue no I didn’t
@@pauldirac808 lmao
😂😂
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
Sam Velasco I vibe so hard as an Econ and Finance major
this when quantum mecanics and special relativity want to mess around
Finally someone can explain this in a simple way! Thanks for all of your videos Andrew!
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!
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!
Anubhav Mishra 😁
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
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!!!
thank you each time for your persistence
Very good explanation! I like how you avoided using the alpha and beta matrices, which is the usual way I've seen it derived.
thanks!
Man allergy season this year is crazy you were sneezing all video, bless your soul.
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!
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!
“Dirac and roll” don’t think I didn’t catch that.
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.
Jaxzan Proditor 😁
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!!!
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
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.
Derive the standard model lagrangian next please!
It's in a fucking book, idiot
General of your mom aren’t they all in books. All he was requesting was to see him derive it there IS NO NEED TO SCOLD HIM. take a look at what you wrote was it even necessary
@@jeremy2719 true, but I think more of the point is that the standard model lagrangian is way too fucking long
@@deeptochatterjee532 I read that long lagrangian has "parts": lagrangiano.blogspot.com/2020/01/lagrangian-for-standar-model-physics.html
That is left as an excercise for the viewer
Exactly what I needed for my Introduction to particle physics course. Thank you :)))
i've just finished watching your video, and it was just amazing, thank you!!
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.
Sweet! Concise and clear, dude you’re the best!
Thanks a lot Mr.Dotson. Was in real need of this.
and suddenly, many years too late, that class on particle physics makes a whole lot more sense.
I understood more than I thought I would. Great job :)
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 TH-cam 😁
Thanks again.
Thanks for making this video Andrew!
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.
"What's up smart people" Heheh, bold of you to assume that I'm smart
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!
Definitely enjoyed this derivation video. Looking forward to its Interpretation!
Dr. Dotson's teaching days of his youth.
- 2019 colorized.
An extremely clear presentation.
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! 😁)
Big thanks for making math avaliable and fun! ❤
😁
Man, you're an awesome teacher!
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! ;-)
Can't wait to Dirac n roll when i actually understand this better💃💃 great video, Andrew!!
U make Four vector algebra look easy.
Grateful☺️
Your mean, easy for you.
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 love hardcore physics videos! Thank you for making them!
Great explanation.
Nice video... good refresher!
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
thanks for giving such knowledge
Phenomenal Job!
absolute ripper great video by sir andrew dotson
I fully understood it. It's wonderful for me
Really elegant in 20 minutes.
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
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.
so cool. keep up the good work!!!!
Man this is an awesome video ❤❤🙏🏼 the best 👌🏽
That was extremely helpful, thanks
such a brilliant vid!
Great job my cousin!!
Damm i got a lot to look forward to in my physics career
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 .
Excellent presentation. Only 1 typo at the anti-commutator relation for u v. Would have been nice to discuss the solutions. Great stuff.
Nice presentation.
Anyone who is interested in the Gamma matrices, read about Clifford Algebras
Ah yes, Clifford, the big red algebra.😂
Your videos are amazing
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)
LordDarkhope really appreciate it. I just always try to address what use to confuse me
@@AndrewDotsonvideos usually, when you try to explain something (that you don't understand) to someone that does not know anything about it, you eventually get it through the process of trying to put it into words. This is my experience with "education" at least.
Keep it up Andrew, the physics majors at the University of Cambridge love your content
Liam Lau 😁😁
The only words I understood was dot product and vector, so I’m basically a fake grad student 😂
Ameen Mahmood he didn’t even understand what the fuck he wrote after somewhere around 20:00 it all went to shit
Maybe you would benefit from Geometric Calculus and Spacetime Algebra to derive the Real Dirac Equation.
geocalc.clas.asu.edu/html/GAinQM.html
geocalc.clas.asu.edu/pdf/Observ-opers.pdf
I would be interested in Mr. Dotson's comments on the criticisms of Dr. David Hestenes regarding the Dirac equation in terms of Geometric Calculus and SpaceTime Algebra.
geocalc.clas.asu.edu/html/GAinQM.html
geocalc.clas.asu.edu/pdf/Observ-opers.pdf
😂😂
That's legendary!! 🤘
I'm currently in ist year of my college and didn't even got a word but still enjoyed the whole video ♥️😍
It's amazing man !
Boutta do a sleep but I caught this boi 5 minutes after upload. Hecc.
gotta watch all of it 3 times now
I suspect Mr Dotson is a magnificent maths tutor because I found all of his explanation utterly fascinating whilst understanding none of it whatsoever . . . .
Physics is always a enjoying thing to watch
Anyone else not know enough math
Im doing Calculus 2 and Physics 1. What the fuck is all of this
Sam Velasco tensor calc, Lie groups and algebra, differential equations and Clifford algebra and prob more
I'm in high school
@@krishnasimha8097 8th grade. Checkmate.
this is kindergarden math
You are a genius. Genius
Great job keep it up
University of Bristol loving your content!!
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.
Hey man awesome content!
I wanna see you derive the Maxwell equations!
Slash notation, what kind of wizardry is this ?
In all seriousness, i liked it how you derived the Dirac Equation.
@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.
Thank you indeed
At 14:08 when you placed the conditional mu=nu under the sum, is that effectively the same as including a factor of kronecker delta sub mu,nu? Thanks
hey men i am having my masters in physics and my professor taught me yesterday the dirac equation.Can you help me out where you made these lectures or any notes(first of all understandable and with proper steps as you did). It would be very helpful for me to prepare my notes.
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.
It's also way more advanced and requires at least some understanding of group theory. Maybe not where I would start if you have to write out tensors.
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
Do in the next video a derivation of the Einstein field equations from the expected value equations in economics.
Wait... So is there insight on the Higgs boson to be gleaned from the Klein-Gordon equation? Or does the whole thing break down because of the potential for negative probability density?
Yo. Your curly brackets. You came from both ways. I'm weirdly impressed
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!
Next year when I get into uni, probably I'll understand your videos.
you wont be doing this for a while
Yeah maybe when you're learning freshman string theory and the universe as a simulation during your second semester
@@haarithio1621 i encourage you to learn it on your own. this is great stuff, i'm learning this outside school
oh yeah i have been waiting so long
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.
the video was great. troubling with the book i am currently reading. so any good reference?
Hey Dotson ! what about the other root ( gamma mu p mu + m) = 0 ?