Quantum field theory, Lecture 11

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 11 we continue the discussion of the Feynman rules for phi4 theory in position and momentum space, prove that vacuum bubbles cancel, and discuss a little renormalisation theory.

[tillerbrady]

Around 32:25, you say we can make a list of all possible disconnected Feynman diagrammes - up to planar isotopy - (or combinatorial equivalence). What does planar isotope or combinatorial equivalence mean here?

[tillerbrady]

What do you mean when you say around 10:05 that scattering theory hints at the fact that there are infinite quantities?

[PeeterJoot]

Around 52:41 you identify the sum as an exponential. That seems to imply the symmetry factors range over all integers [0, infinity] --- why is that?

[manuelaraujo]

Around minute 50 you corrected a formula, saying that it is the value of the numerator of G^2 and not of the whole thing. Does the same correction apply to previous lectures? You wrote before that G^n is computed as a sum over all diagrams with n endpoints, subject to Feynman rules. Should this be the numerator of G^n?

[tillerbrady]

I’m a bit confused by what you mean when you say “every single time we write down a Hamiltonian, we really are writing down a family of hamiltonians parametrised by the cutoff Λ”? I get why we should associate a cutoff to each Hamiltonian, but why is there a family of hamiltonians?

[rafaelbendavid]

Hello, Dr. Osborne! When you mentioned the infinities in physics, and wether any of them have ever been measured, I remembered from my cosmology course that current inflationary model of our universe undergoing accelerated expansion considers this expansion "eternal", its going to be expanding forever, so to speak. Obviously we cant measure this in any conceivable way but might this not be an example of an actual infinitity of Nature?

[charlesbrightman]

"M4" being "space time"
BUT,
"IF" "space" is energy itself and wherever space is, energy is, and wherever energy is, space is,
AND
"time" is the flow of that energy,
THEN for every point in space there would basically be a 360 degree spherical interaction with other "space", and "time" (flow of energy) could be different between the different degrees of space interactions,
SO,
While there might only be 3 dimensions of "space", there might actually be multiple dimensions of "time", not just one, in actual reality.
SO,
"M4" would have to be adjusted accordingly.

Also, things like the speed of light (distance divided by "time"), the speed of light might actually vary depending upon what dimension of "time" one were in.