Ciro Santilli's favorites so far:

Bibliography of the biliograpy:

- physics.stackexchange.com/questions/8441/what-is-a-complete-book-for-introductory-quantum-field-theory "What is a complete book for introductory quantum field theory?"
- www.quora.com/What-is-the-best-book-to-learn-quantum-field-theory-on-your-own on Quora
- www.amazon.co.uk/Lectures-Quantum-Field-Theory-Ashok-ebook/dp/B07CL8Y3KY

Recommendations by friend P. C.:

- The Global Approach to Quantum Field Theory
- Lecture Notes | Geometry and Quantum Field Theory | Mathematics ocw.mit.edu/courses/mathematics/18-238-geometry-and-quantum-field-theory-fall-2002/lecture-notes/
- Towards the mathematics of quantum field theory (Frederic Paugam)
- Path Integrals in Quantum Mechanics (J. Zinn–Justin)
- (B.Hall) Quantum Theory for Mathematicians (B.Hall)
- Quantum Field Theory and the Standard Model (Schwartz)
- The Algebra of Grand Unified Theories (John C. Baez)
- quantum Field Theory for The Gifted Amateur by Tom Lancaster (2015)

Lecture notes found by Googling "quantum field theory pdf":

- www.ppd.stfc.ac.uk/Pages/Dasgupta_08_Intro_to_QFT.pdf "An Introduction to Quantum Field Theory" by Mrinal Dasgupta from the University of Manchester (2008). 48 pages.
- www.thphys.uni-heidelberg.de/~weigand/QFT2-14/SkriptQFT2.pdf "Quantum Field Theory I + II" by Timo Weigand from the Heidelberg University. Unknown year, references up to 2008.
- edu.itp.phys.ethz.ch/hs12/qft1/ Quantum Field Theory 1 by Niklas Beisert

www.hep.man.ac.uk/u/forshaw/NorthWest/QED.pdf web.archive.org/web/20200824083133/http://www.hep.man.ac.uk/u/forshaw/NorthWest/QED.pdf

These seem very direct and not ultra advanced, good read.

Author: David Tong.

Number of pages circa 2021: 155.

It should also be noted that those notes are still being updated circa 2020 much after original publication. But without Git to track the LaTeX, it is hard to be sure how much. We'll get there one day, one day.

Some quotes self describing the work:

Perhaps for this reason Ciro Santilli was not able to get as much as he'd out of those notes either. This is not to say that the notes are bad, just not what Ciro needed, much like P&S:This is a very clear and comprehensive book, covering everything in this course at the right level. To a large extent, our course will follow the first section of this book.In this course we will not discuss path integral methods, and focus instead on canonical quantization.

A follow up course in the University of Cambridge seems to be the "Advanced QFT course" (AQFT, Quantum field theory II) by David Skinner: www.damtp.cam.ac.uk/user/dbs26/AQFT.html

Free to view draft: web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf Page presenting it: web.physics.ucsb.edu/~mark/qft.html

Author affiliation: University of California, Santa Barbara.

Number of pages: 616!

Don't redistribute clause, and final version by Cambridge University Press, alas, so corrections will never be merged back: web.physics.ucsb.edu/~mark/qft.html. But at least he's collecing erratas for the published (and therefore draft) versions there.

The book is top-level organized in spin 0, spin half, and spin 1. Quite ominous, really.

The preface states that one of its pedagogical philosophies is to "Illustration of the basic concepts with the simplest examples.", so maybe there is hope after all.

45 1 hour lessons. The Indian traditional music opening is the best.

10 2-hour lessons.

Lecturer: Leonard Susskind.

Lecture notes: Quantum Field Theory lecture notes by David Tong (2007).

By David Tong.

14 1 hours 20 minute lectures.

The video resolution is extremely low, with images glued as he moves away from what he wrote :-) The beauty of the early Internet.

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.

When the word "advanced" precedes QFT, you know that the brainrape is imminent!!!

Big goal: explain the Standard Model.

Gaussian path integrals.

- web.archive.org/web/20150623011722/http://users.physik.fu-berlin.de/~kleinert/b6/psfiles/qft.pdf by Hagen Kleinert (2015). 1500 pages!
- The Quantum Theory of Fields by Steven Weinberg (2013) www.cambridge.org/core/books/quantum-theory-of-fields/22986119910BF6A2EFE42684801A3BDF
- Quantum Field Theory by Lewis H. Ryder 2nd edition (1996) www.amazon.co.uk/Quantum-Field-Theory-Lewis-Ryder/dp/0521478146
- Lectures of Quantum Field Theory by Ashok Das (2018) www.amazon.co.uk/Lectures-Quantum-Field-Theory-Ashok-ebook/dp/B07CL8Y3KY
- A Modern Introduction to Quantum Field Theory by Michele Maggiore (2005) www.amazon.co.uk/Modern-Introduction-Quantum-Theory-Physics/dp/0198520743

This book really tries to recall basic things to ensure that the reader will be able to understand the more advanced ones.

Sometimes it goes a little bit overboard, like defining what a function does several times.

But Ciro Santilli really prefers it when authors error on the side of obvious.

People are mostly saying you have to be a more of a genius amateur to read it.

ISBN-13: 978-0691140346

lecture 1 mentions that this book is quick and dirty, as one might guess from the title. Ciro Santilli thinks he's gonna like this one.

First edition: from 2003, www.amazon.com/dp/0691010196, ISBN-13: 978-0691010199.

Summary:

This didn't really deliver. It does start from the basics, but it is often hard to link those basics to more interesting or deeper points. Also like many other Quantum field theory book, it does not seem to contain a single comparison between a theoretical result and an experiment.

This is very widely used in courses as of 2020, it became kind of the default book.

Unfortunately, this approach bores Ciro Santilli to death. Or perhaps is too just advanced for him to appreciate. Either of those.

800+ pages.