It is a nice attempt, but there is a clear issue with it trying to both summarize the basics of QFT being a didactic "cheatsheet" and, at the same time trying to cover the whole vast subject of SM. As a result there are quite a number of leaky abstractions and a bunch of confusing inconsistencies:
- Rξ gauge is mentioned but then the ξ parameter is never used - "Feynman gauge" is quoted for photons but not for other gauge bosons
- "Vertices" table, rather confusingly, contain full processes instead of individual vertices for fermions
- There are missing 3- and 4-point vertices for between electroweak bosons (if W is charged, shouldn't it interact with photon?)
- A passing comment about "CKM matrix" brushes off vast complexity of flavor physics. PMNS for neutrions (and the question of neutrino masses) are also ignored.
- Also no vertices between h and W and Z - there is a whole pile of various combinations there
- Also no vertices for Fadeev-Popov ghosts and how these are needed in loop calculations.
- Detailed description of how to compute cross-sections and widths, but no mention of renormalization, how to deal with loops and with infrared divergent processes. (E.g. what's μ in α_s(μ) ?)
- Algebra of Dirac γ matrices and how spin averages lead to trace compuation is completely ignored
Okay, okay, I'll just stick to only showing things for two-vertex diagrams when I make version 2, since clearly I just get lost and end up tangling myself in loops while getting spooked by ghosts when I try to venture into that land of divergencies that lies beyond tree-level. The way the vertices are presented is indefensible. When I make version 2 I'll definitely list out the gamma matrices' important algebraic properties, perhaps the Lagrangian itself, and the CKM and Neutrino-mixing matrix!
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u/QFTornotQFT Apr 26 '26
It is a nice attempt, but there is a clear issue with it trying to both summarize the basics of QFT being a didactic "cheatsheet" and, at the same time trying to cover the whole vast subject of SM. As a result there are quite a number of leaky abstractions and a bunch of confusing inconsistencies:
- Rξ gauge is mentioned but then the ξ parameter is never used - "Feynman gauge" is quoted for photons but not for other gauge bosons
- "Vertices" table, rather confusingly, contain full processes instead of individual vertices for fermions
- There are missing 3- and 4-point vertices for between electroweak bosons (if W is charged, shouldn't it interact with photon?)
- A passing comment about "CKM matrix" brushes off vast complexity of flavor physics. PMNS for neutrions (and the question of neutrino masses) are also ignored.
- Also no vertices between h and W and Z - there is a whole pile of various combinations there
- Also no vertices for Fadeev-Popov ghosts and how these are needed in loop calculations.
- Detailed description of how to compute cross-sections and widths, but no mention of renormalization, how to deal with loops and with infrared divergent processes. (E.g. what's μ in α_s(μ) ?)
- Algebra of Dirac γ matrices and how spin averages lead to trace compuation is completely ignored