Field Theory Fundamentals in 20 Minutes!
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- เผยแพร่เมื่อ 10 ก.พ. 2022
- Field theory is the mathematical language that we use to describe the deepest theories of physics. I'll teach you the basics in about 20 minutes. Get the notes for free here: courses.physicswithelliot.com...
Take my full course on Lagrangian mechanics! courses.physicswithelliot.com...
The most fundamental laws of nature that human beings have understood---the standard model of particle physics and Einstein's theory of gravity---are written in the language of field theory; quantum in the first case and classical in the second. The first field theory that you're likely to meet in your physics classes is electromagnetism, which describes the electric and magnetic fields through which light waves ripple all around us. But electromagnetism is actually fairly complicated; to learn field theory, it's better to start with a simpler example, and that's what I do in this video. I'll teach you the fundamentals using the Klein-Gordon theory of a real, scalar field. We'll see how to write down the Lagrangian, apply the principle of least action to obtain the Klein-Gordon field equation, how to solve it using plane waves, and how relativity is built in from the beginning.
We'll also take a peek at quantum field theory along the way.
Get all the links here: www.physicswithelliot.com/fie...
The principle of least action: • Explaining the Princip...
The Lagrangian for a special relativistic particle: • The Special Relativist...
The Lagrangian for a general relativistic particle: • How Einstein Uncovered...
Tutoring inquiries: www.physicswithelliot.com/tut...
If you find the content I’m creating valuable and would like to help make it possible for me to continue sharing more, please consider supporting me! You can make a recurring contribution at / physicswithelliot , or make a one time contribution at www.physicswithelliot.com/sup.... Thank you so much!
About physics mini lessons:
In these intermediate-level physics lessons, I'll try to give you a self-contained introduction to some fascinating physics topics. If you're just getting started on your physics journey, you might not understand every single detail in every video---that's totally fine! What I'm really hoping is that you'll be inspired to go off and keep learning more on your own.
About me:
I’m Dr. Elliot Schneider. I love physics, and I want to help others learn (and learn to love) physics, too. Whether you’re a beginner just starting out with your physics studies, a more advanced student, or a lifelong learner, I hope you’ll find resources here that enable you to deepen your understanding of the laws of nature. For more cool physics stuff, visit me at www.physicswithelliot.com. - วิทยาศาสตร์และเทคโนโลยี
Yes, I’m very very interested in learning all of it. Your channel is unique in that you’re able to teach very difficult topics in just 20 minutes and not only do you do it by giving us the big picture, but also by getting into the math. You’re helping us learn things in minimum time and with minimum effort. Thank you for your contribution.
Thank you so much Koorosh!
I recognize your remark: "Just want to know all of it". Had that same feeling years ago. But the immense amount of math you need to really study Quantum Field Theory lowered my interest substantially. What you see here is just the very basics. Read about Renormalization.
@@jacobvandijk6525 I believe you. I think I’ll be ok if he skips the lengthy derivations and mathematical complexities as long as he can still help us see the big picture through math.
@@kka107 I agree with you on that, Koorosh. The real mathematical details are only understood by experts, for instance at CERN. We, laymen, must be satisfied with the global contours of the field. May I ask from what country you are? Armenia? I'm from the Netherlands.
@@jacobvandijk6525 Born in Iran, but have been living in the US for the past 28 years. I don’t have a physics degree. Still there’s a great deal of math in electrical engineering which I’m majored in. I always craved to learn modern physics but never had the time to do it the formal way, like by reading a textbook. Elliot’s short lessons are perfect for me. 🙂
10:38 Partial derivatives seem intimidating at first, but here is a simple way to understand them. By the way, this is how I taught them to my students.
You are standing at the base of a hill. The slope changes differently depending on the direction you walk. You want to walk up the hill and retrieve your drone which just crashed on the hill northeast of you.
Let's say the hill slopes upward one foot for every five feet you walk toward the east. This is like the partial derivative, it gives you the slope in the easterly direction only, ignoring any slope to the north (or south). You begin to walk east until you are directly south of the drone, in other words, it is due north of you. Let's say you walked 20 feet to the east. How high are above your starting point? That's easy, it's simply the slope (partial derivative) multiplied by the distance you walked. Remember that the hill rises one foot for every 5 feet you walk. 1ft/5ft x 20ft = 4ft. You are now 4 feet above your starting point.
Now you turn north. At this point the hill is much steeper, sloping upward one foot for every three feet you walk toward the north. Again, this slope is like the partial derivative, it gives you the slope in the northerly direction, ignoring any slope to the east or west. This time you walk 15 feet to reach the drone. 1ft/3ft x 15ft = 5ft. You are now 9 ft up the hill, 4ft from walking east, and another 5 from walking north.
You could have walked north first then east in which case you would have to know the slopes at two points, the first to the north of your starting point then the slope to the east at the point where you turn east.
Regardless of the route you take, using the slope in one direction at a time allows you to calculate the height of each leg of your walk which you then add together to get the total height. Just like this imaginary walk up a hill, partial derivatives allow you to calculate changes in steps by calculating how the change in one variable affects the change in your target variable.
The first partial derivative on the right side tells you how the field changes with position, while ignoring the position (just like we ignored the slope northward while walking eastward). The other partial derivative tells you how the field changes in time while ignoring any changes from position. In this way the total change can be calculated.
Wayne Y. Adams
B.S. Chemistry
M.S. Physics
R&D Chemist (9yrs.)
Physics Teacher (33 yrs.)
Glad to see you Sir
I'm very bad at math, i have high difficulties in learning physics, maybe due a lack of will at same time. And i understood very well.
You've just taught the Lagrangian in the most straight forward and intuitive way that I've ever come across, and did it as a sidenote to a main topic. Thank you for your brilliant teaching. Keep up the good work.
Thanks Jacob!
@@PhysicswithElliotHello what math Should i specially need to learn to understand this video (especially the field theory part) I kinda know how to differentiate and integrate what else i need to learn? I will be happy if you can guide me
Jeez, was it really? I couldn’t understand it at all 😭
The square is always so funny to me because the first time I saw it in a book I thought it was a symbol that couldn't load properly and I kept closing and opening the book until I decided to finally search for the "missing" symbol online and found out that there was never a problem. Please upload more, this was awesome!
d Alembertian, second partial with time. Shorthand.
You're very talented at presenting and teaching. I've never seen such highly quality, clear explanations for such advanced topics. The animations and drawings add an aesthetic touch which makes it even better. You deserve so much for this kind of dedication man. Keep it up!
Appreciate it!
I second this.
This is about 2 lectures worth of work in the maths/physics degree I took. You presented it in 20 minutes, and I genuinely gained more from this than those lectures. Incredibly succinct and clear. Really good video.
So exited you are started posting these videos on Field Theory now, together with the handouts.
All of your videos and handouts, not shying away from math, are of an exceptionally clarity and even entertaining.
They close the gap between (semi)popular video´s and semester long university courses you sometimes too can find on YT.
But the latter, how good they may be, are very long and you easily lose the full picture of it.
I studied Theoretical physics in the eighties and then drifted to ICT.
Last couple of years taking it up again and am hoping to get some more insight into QFT, which we barely touched at the time.
After some MIT Moocs, am now into the very good book of Robinson: Symmetry and the Standard Model. It goes slow, but then I have the time.
Your videos so far and the ones hopefully to come, are of tremendous help in getting a fresh expose on the subject.
Proud to be one of your patreons.
Thank you so much Bart! I'm glad it's helping with your QFT studies. It's a tough subject!
I agree! the explainations are very clear and consice
This is everything I've ever wanted out of a physics education.
Thank you so much, man. Plus this video reminded me to buy in on your patreon now that my financial aid refunds came through (I certainly feel comfortable calling it an educational expense lol)
May many more follow in your footsteps. Think of the things we could achieve with the fruits such efforts bear across even one generation.
Many thanks!!
There are many science channels on TH-cam which get into the detail of the topic but don't quantitatively explain the concepts. Since I like getting into the rigors of calculations, your channel helps me a lot in gaining interest in new topics. Thank you Elliot!
This is, without exaggeration, one of the best videos I've ever seen. I'm a first year PhD student in physics, and this connected so many distant ideas and everything just clicked in place. Thank you so much!!!!! You method of explaining is extraordinary, and also really appreciate you going through some of the math and rigor, since a qualitative description can only go so far. :D
You crammed a lot of Physics into 20 minutes, Elliot!
Herbert Goldstein concludes his "Classical Mechanics" with Field Theory.
Michael Faraday's concept of the electric and magnetic fields, and his collaboration with James Maxwell were the first steps in a modern unified field theory.
Really appreciated this video!
This finally helps me to connect the dots of many concept i encountered during my physics degree, without having to take a full semester theoretical physics class.
I'd really appreciate a video on spinors' lagrangian too.
Wow, this is amazing. I always wanted to learn about the Field Equations and now I have the basic idea where it all come from. Please continue with this series. This definitely guaranteed a sub.
I love how so many areas of physics and mathematics come out of something so elegant yet powerful
This is quite impressive, even for someone who has studied the field its lovely to gain new insight on the subject matter.
Absolutely incredible. Didn't think it could be possible to explain this topic with such clarity and conciseness while maintaining engagement through the narration and great aesthetics. Thanks a lot
That's actually a GREAT explanation. I can't think of anything you left out. You provided all relevant information in an easy to digest way. It was both formalistic and intuitive at the same time. I have no words, probably the best physics explanation video I have ever seen.
Its incredible the quality of content you have created that doesn't leave any gaps in math or understanding. I'm beginning to look forward to every video you put out :) keep up the good work! Well maybe not a completely rigorous math lesson but definitely super motivating to check out your notes.
Impressive work as always! Your ability to explain even one of the most complicated things such as field theory is genuinely fascinating!
Please, Elliot, I need "the rest" for the other spins as well. All insights in this topic is wonderful! Thank you so much for your efforts !!!
Outstanding. I've heard tons of lectures on physics and field theory (I am a physicist myself), but this is just perfect.
If I ever end up teaching this subject I will come back to this.
Thank you.
Thrilled to see this on TH-cam. I always was watching the pop science clips but my search was giving zero results on formulas explanations in the TH-cam. The more I searched the less I found. And I am not so in favor of reading the boring textbooks. This is well delivered. Now I can self teach a bit real field math. Thank you.
Superb work!!! As a physics student, I can say videos like these are extremely usefull for understanding the concept behind many tools we use. A lot of times this point of view of physical theories is lost in many textbooks in favour of mathematics and calculus (which is usefull too), so it’s extremely helpfull that people like you make this kind of videos.
Pd: english is not my native language, so sorry for any mistake I might have made in the coment :)
Thank you Fuencisclo!
This has been a great video, it is the clearest explanation I've ever heard actually. Please do continue on field quantization and also the fields of other spins.
I love physics for the sake of it, even though it is not what went for college. For these twenty minutes really helped me excited about field theories. In the begginning, I was little hesitant to look unto QFT due to the weird notations, but now you gave me a push to dive into. I love your videos Ellisiot. Thank you alot.
I started reading a QFT book some time ago and while I was able to progress in the frist chapters, it got so dense that I couldn't really see the big picture. Your videos help a lot!
Looking forward to see more details on spin 1/2 and 1 field theories :D
Thank you! It’s hard to find such a superb tour of this subject that includes the basic mathematical concepts. Lots of your audience have studied introductory quantum physics, but never got to see the next level.
You did an amazing work. Thank you by the effort and the clear explanation.
I'm taking a one-semester introductory QFT course and your video just appeared in the recommended videos. I found it amazing! I've already subscribed to the channel to wait for the sequence!
your deep understanding of the physics principle is fantastic.
You're natural born teacher. I'm not unfamiliar with the topic (as far as a non-physicist can be), and still I feel I understand the topic more clear than ever before. Thank you.
Incredible that we have access to content such as this video. Thank you very much!
This content is amazing, I can´t thank you enough for all this hard work and yes, we want to learn more about everything ;)
Thanks a lot Andy!
Finally, someone came up with an actual physics video with math. Thank you!!
Incredible stuff, I wish I had this resource during undergrad. It would've saved me countless hours trying to understand Landau's field theory book. I think I learned most of this from Dirac's GR book but it was almost as impenetrable.
Very nice video. I'm takin qft next fall and this was a good intro. The derivation with the differential of curly L broke the pace a bit since it wasn't immediately obvious what steps you were taking between subsequent results, but everything flowed smoothly otherwise. I hope you continue to make videos on the topics mentioned at the end. The videos make field theory seem very accessible with basic undergraduate knowledge.
This was amazing and super informative. Everything made perfect sense to me as someone taking the second term of quantum mechanics. I would love more of this.
Glad to hear it!
After studying tensors, I am now understanding this video. You say things that relate different areas of science: like the math that is used in both QFT and cosmology. I can't really put it into words, but thanks. The math of Dirac fascinates me.
This is the best presentation i've seen so far of Field Theory. Wish i had it earlier on my studies of the subject. I will certainly recommend this video in my department.
Your video was absolutely incredible. Thank you so much. And yes, I am tremendously intrigued by the other things you mentioned at the end and will deeply appreciate it if you make videos on them as well.
Thank you very much for this amazingly clear explanation. I never had a field theory lecture and thank's to you I now understand the link of Lagrangian mechanics and Klein Gordon equation, and I am so glad I do !!
I'll definitely be a patron to find more videos on field theory. Your channel is awesome
Elliott, you are the best! This is the best and most coherent intro I heard of field theories.
Your content is gold.
Please do one on the Dirac field.
Thank you so much!
Thanks Gilad!
Please continue on with complicated subjects like these! It’s hard to understand the resources elsewhere, so this video helped SOOO much!
Very elegant explanation. thank you .
Yes please continue. It would be nice to see real simple examples illustrating the math and concepts.
Just discovered your channel and already binge watching all your videos. Keep up the amazing work!
Welcome Stefano!
This channel is just pure gold. Although I am a high school student and did not understand most of it, I really enjoyed watching the full video. Big appreciation to you.. Wish you for amazing success..
Thanks Saurav! Check out my "help room" playlist for more introductory videos while you're working your way up to the more advanced stuff!
@@PhysicswithElliot Sure, Elliot.
I have a very good lecturer that taught this material to us (in my opinion) very well. But it was very easy to get lost in the detail and forget the big picture. This video sums up all the key points of about 6 hours worth of lectures unbelievably well. Having watched this video after struggling to grapple with my uni's material, I feel soooo much more confident.
Thank you so much for this video AND the notes. You are awesome Elliot!
Excellent whirl wind tour. It helps me understand the big picture behind the stuff I’ve studied.
I wish I'd had you as a math professor when I attended college: your explanations are super-clean and high quality.
I would greatly appreciate if you'd "go down the rabbit holes" of the notations describing particle spins and their semantics.
Thanks for the fantastic videos. I would love to learn more about field theory and in particular about Dirac’s equation.
Amazing, as a senior physics student this is very accessible coming from undergraduate courses.
I WANNA LEARN MORE! This was done so elegantly and was so incredibly helpful. My professor explaining this was the first time I'd heard of Field Theory, this video cleared my many misconceptions up a ton. Thank you!
Glad it was helpful!
You’re my new favorite youtube channel! You’re also very great at explaining this in simple terms! Keep making good content man! 👍🏼
Thanks Jenn!
This was an amazing introduction to field theory! Thank you!
Amazing video! Keep up this level of content. It is advanced yet easy to follow
Thanks Sean!
it's a king of magic !!! Thanks for these beautiful explanations !!!
Perfect !!
If it is possible to conduct two dedicated series, one for special relativity and another for general while diving into details , that would be great !!!!
Thanks for these videos in all cases :)
Excellent introduction to field theory! Thanks!
Yes, please do show us more classical field theories!
You do have an amazing way of imparting knowledge. You obviously understand the material quite well.
Thank you. 🤘
Still amazed with the elegant presentation! Cheers!
amazing video, this is a very tough subject and you make it very friendly!
thank you for this great content
so much enlightening! Thank you💖💖💖
I really wanted to thank you because you pass by the mathematical developments in a logic way that really help to understand
Amazing video, love the way you present the math!
LOVED this video, thank you ! If you would just continue explaining quantum field theory right on from here it would be fantastic !
This video is gold and a deeper dive in QFT in a similar fashon would be even more gold
Please continue this series!
Would love to see a follow up video outlining QFT. Very concisely explained; well done!
This is an amazing video! Thankss! I completed my theoretical Physics msc recently. Your research papers too are very exciting for me!
Your explanation is so GREAT. If I had these videos in my PhD years, probably I would not give up my journey in theoretical physics........
Why did you give up?
Elliot, I love you videos so much that if you released a series of 20 lectures on any given topic I would watch them in one sitting. Absolutely brilliant stuff. On a side note, what's the tablet/software you use to write the formulas in you videos (at least the previous ones)? The letters always seem so nice and even, lines are always straight etc.
Thank you! I made those with the app Procreate!
You make these topics much, much easier to understand than my undergraduate physics tutors did 40 years ago. I seem to go through your videos saying "Oh, _that's_ how that works!" about every 2 minutes!
❤ you are great you made it possible to understand such topics
Please continue these videos! They have really helped me when studying Theoretical Physics at the University of Birmingham and I really would like to see a video about spin ½ and 1
Thanks Joao! Glad it helped!
I love this channel so much, thank u for ur effort dude ❤️
I've just started studying quantum field theory and finished my courses on general relativity and have been extremely curious about what is to learn and confused about how my professor teaches. I love this video. Please make more like these describing different spin particles, quantum fields and especially spin 2 fields. It's all so interesting. You explain extremely well and have amazing editing. You've earned a sub from me. Thank you.
If you’re interested in spin 1/2 field I’ve made a video on it on my channel if it helps
This was fabulous I cannot say that enough unbelievably well done
Fastest 20 minutes in this year so far.
Pls do make more videos on Dirac field in future
Amazing pedagogy here. Yes please, more field theory videos!
Excellent video I will used in my classes. Excellent job.
Thanks Jose!
This was such a beautiful video! Thank you for such a great production
Thanks Maxx!
amazing thank you so much ! helping me through my class of field theoretical aspects of GR
Pls continue, ur course’s gonna be cool
Awesome lecture! Succinct and very clear! Thanks
Excellent, excellent explanations for what even universities struggle to teach in an intuitive, easy-to-grasp manner. Great job with the concrete examples, the explanation of physical meaning and intuition behind the maths, the overall structure of the lesson, the motivation behind the concepts and maths, the animations to illustrate the point, the reminders of what we’re measuring - I cannot express just how excellent this is as a science communication and educational video!
Much appreciated!
Just found this video. Great explanation of the topic. Beyond subbing, I checked out your Ph.D. Dissertation. I dove into a few chapters while skimming through it (where I could understand). Would love to have you teach us all about it. Thanks!
This was amazing!!!! Learned more from your channel than my 2 years of college
Wow this was really well done. Although I found it to be a bit too advanced at times. Will have to give it a few rewatches 😁
You forgot your base e's at 16:30
This video is smooth, and the videos make reviewing graduate physics more fun!
Yes, I'd love more videos on field theory!
Wow, I love it, I think you just filled a couple holes I had in my understanding, and answered some questions I’d actually been wondering about for the last month or so. All in all this was not only great in that regard, but I think covered the math pretty well and in such a way that I’m going to have to reference and rewatch this video several times as I keep absorbing everything here. Great work!
Glad it helped Christopher!
Brilliantly explained, thank-you!
Thanks Ted!
Explained twenty times better than anyone before you!! Ty
such a wonderful and amazing and informative and well structured tutorial! Thank you very much. subbed! :)
Excelente Work. Thank You!
better explanation ever! Congrats!
Hi! Best explanation of KG eq i ever found!
The best video ever!!! Thank you!!! We want more! Much more!
Thanks Yossi! New video coming soon!