Ciro Santilli This is a bit "formal hocus pocus first, action later". But withing that category, it is just barely basic enough that 2021 Ciro can understand something.
By: Tobias J. Osborne.
Lecture notes transcribed by a student: github.com/avstjohn/qft
18 1h30 lectures.
Followup course: Advanced quantum field theory lecture by Tobias Osborne (2017).
Bibliography review:
- Quantum Field Theory lecture notes by David Tong (2007) is the course basis
- quantum field theory in a nutshell by Anthony Zee (2010) is a good quick and dirty book to start
Course outline given:
- classical field theory
- quantum scalar field. Covers bosons, and is simpler to get intuition about.
- quantum Dirac field. Covers fermions
- interacting fields
- perturbation theory
- renormalization
Non-relativistic QFT is a limit of relativistic QFT, and can be used to describe for example condensed matter physics systems at very low temperature. But it is still very hard to make accurate measurements even in those experiments.
Defines "relativistic" as: "the Lagrangian is symmetric under the Poincaré group".
Mentions that "QFT is hard" because (a finite list follows???):
There are no nontrivial finite-dimensional unitary representations of the Poincaré group.But I guess that if you fully understand what that means precisely, QTF won't be too hard for you!
Notably, this is stark contrast with rotation symmetry groups (SO(3)) which appears in space rotations present in non-relativistic quantum mechanics.
www.youtube.com/watch?v=T58H6ofIOpE&t=5097 describes the relativistic particle in a box thought experiment with shrinking walls
- the advantage of using Lagrangian mechanics instead of directly trying to work out the equations of motion is that it is easier to guess the Lagrangian correctly, while still imposing some fundamental constraints
- youtu.be/bTcFOE5vpOA?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3375
- Lagrangian mechanics is better for path integral formulation. But the mathematics of that is fuzzy, so not going in that path.
- Hamiltonian mechanics is better for non-path integral formulation
- youtu.be/bTcFOE5vpOA?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3449 Hamiltonian formalism requires finding conjugate pairs, and doing a
- symmetry in classical field theory
- from Lagrangian density we can algorithmically get equations of motion, but the Lagrangian density is a more compact way of representing the equations of motion
- definition of symmetry in context: keeps Lagrangian unchanged up to a total derivative
- Noether's theorem
- youtu.be/cj-QpsZsDDY?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3062 Lagrangian and conservation example under translations
- youtu.be/cj-QpsZsDDY?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3394 same but for Poincaré transformations But now things are harder, because it is harder to describe general infinitesimal Poincare transforms than it was to describe the translations. Using constraints/definition of Lorentz transforms, also constricts the allowed infinitesimal symmetries to 6 independent parameters
- youtu.be/cj-QpsZsDDY?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=4525 brings out Poisson brackets, and concludes that each conserved current maps to a generator of the Lie algebraThis allows you to build the symmetry back from the conserved charges, just as you can determine conserved charges starting from the symmetry.
- quantization. Uses a more or less standard way to guess the quantized system from the classical one using Hamiltonian mechanics.
- youtu.be/fnMcaq6QqTY?t=1179 remembers how to solve the non-field quantum harmonic oscillator
- youtu.be/fnMcaq6QqTY?t=2008 puts hats on everything to make the field version of things. With the Klein-Gordon equation Hamiltonian, everything is analogous to the harmonic oscilator
- something about finding a unitary representation of the poincare group
Interactions.
Dirac field.
Dirac equation.