1/ The Einstein Energy-Momentum Relation can be straightforwardly turned into the `Klein-Gordon Equation.`
Why’s that important?
The KG-Equation describes spinless particles of any charge! †pic.twitter.com/mboQngOfat
PhD student of Theoretical Particle Physics @UCIrvine l @NSF Fellow l Physics & Math Animations l Patreon: https://www.patreon.com/inertialobserver …
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1/ The Einstein Energy-Momentum Relation can be straightforwardly turned into the `Klein-Gordon Equation.`
Why’s that important?
The KG-Equation describes spinless particles of any charge! †pic.twitter.com/mboQngOfat
2/ If you use natural units (author’s note:
) where ℏ = c = 1, and replace `E` and `p` for their quantum operators...
pic.twitter.com/boG9B2mSWm
3/ You’ll find that the equation reduces to below. Very serendipitiously, the *d’Alembertian* pops up and we can get a Lorentz-Invariant relativistic equation...pic.twitter.com/kZn95C6Guc
4/
The Klein-Gordon Equation!
pic.twitter.com/r9vvD1fFQA
5/ Why is this important? The KG-Equation describes spinless particles of any charge. However, unlike other wavefunctions, the norm squared |φ|^2 won’t give you a probability amplitude here, but it will give you a *charge density.*
6/ † It’s important to note though: for common spinless particles, e.g. the pion, the KG-Equation doesn’t tell the whole story because quarks & gluons also experience the Strong Force.
Oh well!
pic.twitter.com/2R9MhQslWW
I’m not a fan of the myth that we tell the kids that we “know” that confined particles are a composite state of quarks/gluons when in reality quarks and gluons are just I’ll defined when the coupling is strong
That’s a very good point. There’s a lot of space for more to happen inside. I’ll keep that in mind by adding in some nuance
Maybe a thread on Feynman diagrams would be a strong point to emphasize second order interactions
it would but unfortunately this problem is non perturbative :’( which is a direction of research I’ve been fascinated with lately
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