Quantum field theory, Lecture 2

This winter semester (2016-2017) I am giving a course on quantum field theory. This course is intended for theorists with familiarity with advanced quantum mechanics and statistical physics. The main objective is introduce the building blocks of quantum electrodynamics.

Here in Lecture 2 I discuss classical field theory and the least-action principle.

[columbiafermi]

All physics courses need to be taught where there is enough black (green) board space.
The conservation of energy demands this!
These are great lectures, very well organized, understandable, reminds me of Wolfgang Ketterles'
graduate course on Atomic Physics at M.I.T /8.421.

[simonb.]

Thank you for making such a nice lecture accessible to everyone!

[PeeterJoot]

Minor "typo" around 40:01 -- delta phi_a was both inside and outside the braces.

[jasminecruickshank]

This is so great and also strangely relaxing

[hookups]

I think there's an error when you define the Lagrangian related to the Klein Gordon Field (around 50:00). In "3D form" it's correct, but when you write it in covariant form, a scalar product (with covariant and contravariant derivative) must appear, and not "d mu phi " square. That's why you make a mistake when you calculate the term in Euler-Lagrange equation right after. Anyway, it's a really great course, thanks for sharing it.
A physics student from France

[rv]

"c-number is a ridiculous thing to write" - Finally a physicist admitting this!

[jerrycai]

Hi Prof! A bit of confusion at 1:18:05 where you write down p_j(t) -> \dot{\phi}(t, x). According to the formula of p_j(t) on the left blackboard, shouldn't this result be zero since \pi multiplies zero equals zero? And if this is the case, how am I suppose to understand the physical meaning, such that for a fixed q, the corresponding p is 0 - although everything make sense again after assembling back to the continuous case.

[physicsguy]

Nice lecture. Two questions: at around 1:08:50, you discuss getting a lagrangian for a discretized field. You're viewing the field values at the discrete points as the generalized coordinates, so are you essentially viewing the field as just N (number of sampled points) degrees of freedom that obey some Euler Lagrange equation? By writing the lagrangian as an integral of a lagrangian density, it seems you are assuming that the Lagrangian is a sum of local terms that depend only on the field value at each point (and its derivatives). Is this truly an assumption, or does it follow from something for fundamental? I could imagine some system of degrees of freedom where the potential energy cannot be written as a sum of local terms, like a system of interacting point charges, in which case the lagrangian can not be written as a sum of local terms like the example you're talking about.


Thanks for all this content. It's really quite nice.

[termitori]

at 41 the term delta phi a is in double... (error)

[tiamatbenoit]

Thank you, finally a course in quantum field theory explained in mathematical terms

[balderus]

I really like your lectures so far. Are the exercise sheet also publicly available?

[michaelgonzalez]

Quantum symptom looks at electrical (r/c/e) the formula for quantum soup theory

[kostrahb]

Great lecture and very elegant theory behind :)
By the way, are there any applications of the mathematical theory behind QFT on data compression?
(I have caught some applications of variational analysis on data compression and as you said, QFT is basically an extension of variational analysis, it might be interesting topic)

[sainte]

Hi there!!!Soo interesting lectures and notions.Prof. I would love to know what you would answer to a young person who is interested in physical sciences and wonders what they are...Would you somehow let your love of QFT influence your answer?How?

[achiltsompanos]

Tobias, what a great course. However, it would be nice to have access somehow to the exercises. Can we do that? thx

[jasonc]

21:01 Physical systems are noisy, lol. And when you want to concentrate on something, they annoy you. *cough* LIGO

[samapanbhadury]

Why do we discretise in space only and not in time? (between 1:06:00-1:08:00)

[sdu]

How can we tell if a particular field is scalar, vector etc.? For eg. pion, a meson (quark + anti-quark) is a vector field, but a Higgs boson is a scalar field.

[javierrendon]

when you gave examples of fields, for the case of the vector case you wrote pions, aren't they scalar fields?

[jcollins]

Picture an infinite fundamental particle static to the CMB. It’s infinitely small and infinitely expressed. Every universe expresses this particle infinitely. Each infinitely expressed particle expresses every matter, force, field, and everything else humans don’t know about are expressed probability wise infinitely. It’s simply probability that lets us experience them. Duh