What are Quantum Fields? | Introduction to Quantum Field Theory

In this video, we will discuss what makes a quantum field "quantum" and give a soft introduction to quantum field theory.

Contents:
00:00 Introduction
03:00 Quantization
05:36 Appendix

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[MrNerdpwn]

I'm a masters student in physics and these videos are a blessing. These videos are like a nice recap after taking the whole course!!

[likaspokas]

this channel literally summarizes each subject of physics in less that 10 mins .
This channel is underrated !!

[ericrechberger]

Honestly, this channel is truly excellent, every video is clear and easy to understand

[Hampardo]

So good! It's just a teaser for me though. Can't wait to learn this for real in college next year.

[tanchienhao]

omg i have been hoping youd do this!!! thanks so much! please continue

[rahulpratappatel]

This video made me think some of the concept's which I haven't thought during my QFT lectures.

[mohameda.]

As usual, great work, you really sum it up in a very short bite size learning video. Just a tiny thing not even sure if it makes sense, @ 7:23 I guess the denominators should be 2k then the role of the integration along with the Dirac delta is to both disappear from the expression while converting those k’s into ω’s

[codingphysics]

It's been a while since I've took lectures in quantum mechanics. But your video was very conclusive and understandable. I would be happy to see more videos on this.
(If I remember correctly, the operators _a_ and _a*_ are actually the creation and annihilation operators.)

[scottdc]

Thank you for your time and effort making these videos, quick question. In an atom is the field between the electrons and nucleus considered a quantum field?

[Zxv]

This is a great video, but for the life of me I could not understand the intuition behind the delta function tick at 7:04. I understood the sum and the delta function involving the roots, but dividing by the magnitude of the derivative was completely opaque.

Took me a little while to work it out, but with the help of Wikipedia and StackExchange, I finally got it. It turns out you obtain the formula simply by replacing a δ(f(x)) in a standard integral with a sum involving integrals in a small region around only the roots of f (since the delta function is 0 outside of δ(0)). Then you Taylor expand f around each of the roots (the constant term vanishes when expanding around roots). You can ignore terms of order 2 and higher by arbitrarily shrinking the integration region, and the order 1 term can be handled by applying the scaling property of the delta function. The absolute values arise because δ is an even function.

[orchoose]

Hey, why is there integral in eq. for Pi you are writing at 4:27. Right above it you say Pi is partial time derivative of Phi. Where does the volume integral come from?

[bezbezzebbyson]

What is the motivation behind the quantization process of fields? Why they become operators and what does it act on or calculate? Wiki page on second quantization introduces qft as a generalization of many-body qm and got to field operators from there. That convinced me but how does that connect to canonical quantization?

[nellvincervantes]

Question sir. How can you add different quantities such as

-k^2 = m^2

And

k*^2 + k(vector)^2 = m^2 ?

[joeharmon]

In all of that did you tell us what a field is?

[namesurname]

Very nice and clear video as always. But I still got a question. Why in first quantization observables are expressed by quantum mechanical operators and in second quantization are not, with consequence the fields to be operators? Thank you very much for your time your videos are very helpfull!

[sword]

what are the prerequisites to study quantum field theory on my own.
I took a : graduate classical mechanics course, a course in electromagnetism(without tensors and stuff), a quantum mechanics course at the level of griffith. is there some good resources for classical field theory?

[tanvirfarhan]

what level of mathematics are you writing?

[jacobvandijk]

So what's a quantum field in words?

[endaleabebekumsa]

Okay the last must be God's field!