Uploaded December 2019 | Updated September 2026, 14 hours ago
In this video, I show you how to derive the general decay rate formula. This is the formula that allows you to compute decay rates in quantum field theory from the Feynman amplitude.
My Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
S-operator Video:
youtu.be/OXVfJtwzaog
Differential Scattering Cross Sections In Quantum Field Theory:
youtu.be/HqOetWTHeGs
Deriving The Feynman Rules For QED Video:
youtube.com/watch?v=ToL-37wnHZw
Superfluid Helium Resonance Experiment video:
youtu.be/unUNQNmuvUQ
Notes:
- In the final formula for d(dT_fi)/dVdt, the k-bar_2 isn't supposed to be their. The formula is correct if the that is ignored.
- Throughout this calculation, I use the letter "k" for momentum variables, but in the boxed formulas at the end, I switch to "p" for the momentum variables. They refer to the same thing. I noticed this during editing, and I decided not rerecord, because it isn't an error in the math, and isn't liable to create much confusion.
- In the limit that the f(k)-function goes to the delta function that fixes the average, k-bar, to be the exact momentum (i.e. the limit of plane wave incoming particles that therefore have specific momenta), the formulas given here become exact, because the rough equality given at 10:04 becomes exact. This limit is what's consistent with the derivation of the standard Feynman rules. Therefore, these formulas taken exactly are compatible with the standard Feynman rules.
In this video, I show you how to derive the general decay rate formula. This is the formula that allows you to compute decay rates in quantum field theory from the Feynman amplitude.
My Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
S-operator Video:
youtu.be/OXVfJtwzaog
Differential Scattering Cross Sections In Quantum Field Theory:
youtu.be/HqOetWTHeGs
Deriving The Feynman Rules For QED Video:
youtube.com/watch?v=ToL-37wnHZw
Superfluid Helium Resonance Experiment video:
youtu.be/unUNQNmuvUQ
Notes:
- In the final formula for d(dT_fi)/dVdt, the k-bar_2 isn't supposed to be their. The formula is correct if the that is ignored.
- Throughout this calculation, I use the letter "k" for momentum variables, but in the boxed formulas at the end, I switch to "p" for the momentum variables. They refer to the same thing. I noticed this during editing, and I decided not rerecord, because it isn't an error in the math, and isn't liable to create much confusion.
- In the limit that the f(k)-function goes to the delta function that fixes the average, k-bar, to be the exact momentum (i.e. the limit of plane wave incoming particles that therefore have specific momenta), the formulas given here become exact, because the rough equality given at 10:04 becomes exact. This limit is what's consistent with the derivation of the standard Feynman rules. Therefore, these formulas taken exactly are compatible with the standard Feynman rules.
