### Peter Phillips

Shared publicly -Random reading part 2 - probably the most comprehensible introduction to quantum field theory I've found so far. I got a vague understanding of how a "quantum field' is built up from scratch. This reading was inspired by the statement "Particle physics isn't about particles".

I learned that many of the "quantum" properties of the field fall out of the math/analysis. e.g. spin, anti-particles (relativity required), fermion/boson, even the resulting 'forces' caused by the field (including when attracting/repulsing). (It does depend on the starter ingredients: e.g. scalar, complex, 4-vector and deciding if you'll include special relativity or not). (And picking the Langrangian, also)

What I didn't learn (thanks to my advanced gloss-over--90%-details reading) is exactly how quantization happens. Yeah, sure, you can throw together a matter field, couple with "electric" field, and maybe you need to throw in the mass of electron as a parameter (or Higgs-ify it). But why do you end up with only one electron mass? (Or charge)?

As for it "not being about particles"--the shortest answer, is (duh), QFT is about the field. The next shortest answer is...hard to explain. The "particles" as such are created/destroyed by applying operators to the field. But what is created is kind of like a vibrational mode and might be localized in space, diffuse in momentum or vice-versa. The operators are analogous to usual operations (addition, multiplication) but operate on an infinite-dimension Hilbert space. So...a bit more complicated.

This leads to statements like "Well, we can define a particle-counting operator which counts the 'particle' eigenstates and then show it is properly Lorentz (observer) invariant, so, there's your particles."

It's actually exciting. Although the exploration of field theory requires heavy-duty particle accelerators, the math can can also be used in condensed matter. This could lead to some seriously awesome nanoscale devices, one day.

Disclaimer: my statements are only as accurate as 90% skimming will allow.

http://www.damtp.cam.ac.uk/user/tong/qft.html

I learned that many of the "quantum" properties of the field fall out of the math/analysis. e.g. spin, anti-particles (relativity required), fermion/boson, even the resulting 'forces' caused by the field (including when attracting/repulsing). (It does depend on the starter ingredients: e.g. scalar, complex, 4-vector and deciding if you'll include special relativity or not). (And picking the Langrangian, also)

What I didn't learn (thanks to my advanced gloss-over--90%-details reading) is exactly how quantization happens. Yeah, sure, you can throw together a matter field, couple with "electric" field, and maybe you need to throw in the mass of electron as a parameter (or Higgs-ify it). But why do you end up with only one electron mass? (Or charge)?

As for it "not being about particles"--the shortest answer, is (duh), QFT is about the field. The next shortest answer is...hard to explain. The "particles" as such are created/destroyed by applying operators to the field. But what is created is kind of like a vibrational mode and might be localized in space, diffuse in momentum or vice-versa. The operators are analogous to usual operations (addition, multiplication) but operate on an infinite-dimension Hilbert space. So...a bit more complicated.

This leads to statements like "Well, we can define a particle-counting operator which counts the 'particle' eigenstates and then show it is properly Lorentz (observer) invariant, so, there's your particles."

It's actually exciting. Although the exploration of field theory requires heavy-duty particle accelerators, the math can can also be used in condensed matter. This could lead to some seriously awesome nanoscale devices, one day.

Disclaimer: my statements are only as accurate as 90% skimming will allow.

http://www.damtp.cam.ac.uk/user/tong/qft.html

A Cambridge University
course with lecture notes, covering the canonical quantization of
scalar fields, Dirac fields and QED.

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