费曼图
- Interpret the Schroedinger equation for the harmonic oscillator in terms of Feynman diagrams.
- Check what happens when I add labels to the ends and then divide by the symmetries. How does that relate to the coefficients?
- Does a vertex of a Feynman diagram, bringing together four inner legs, express a foursome, and thus define something? Are the inner legs expressing what is defined, and the outer legs what is undefined, "from beyond"?
- Understand Feynman diagrams in terms of the Birdtracks book.
- Is Cvitanovic's concept of negative dimensions in Lie theory related to the duality of counting forwards and backwards?
- Understand 书: Predrag Cvitanovic. Birdtracks, Lie’s, and Exceptional Groups. How does he use Penrose graphical notation to classify the classical Lie groups?
- Is there any relation between Penrose's graphical notation and Feynman diagrams?
- Feynman diagrams are based on the combinatorics for Hermite polynomials. What is based on the combinatorics of the other Sheffer polynomials? Do they add additional perturbation terms, such as {$\lambda^4 + \mu^6$}?
- Think of Feynman diagrams as describing divisions of everything based on vertices. These divisions can be variously understood.
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读物
Ideas
Wick's theorem.
- Goal of calculation is to reorganize the time ordered operators so that they are normal ordered operators, in that the particle creation appears before the particle annihilation.
- Wick's contraction interprets the double factorial in terms of pairs of connections.
Feynman diagrams
- In Feynman diagrams, charge means that lines are oriented. Chargeless are not oriented.
- Feynman diagrams distinguish local changes (at vertices) and nonlocal changes (motion). Local changes occur at "the present".
- Feynman diagrams are thought of as morphisms in monoidal categories.
- Feynman diagram sets up the grounds for the foursome, fivesome, sixsome, sevensome. The incoming wires are Why and How and outgoing are Whether and What and thus the two causalities are related. But the directions of the causalities can get twisted around by the various divisions.
Notes
Feynman diagrams
- Mathemaniac. Green's functions: the genius way to solve DEs.
- Dirac delta distribution is a probability distribution that models certainty. Thus it is discontinuous as a probablity density because it is zero everywhere except for at a particular point. So its value is discontinuous at that point both from the left and from the right.
- Virtual particles do not have speeds - thus do not conserve momentum or energy.