The deconstructed Standard Model equation
symmetrymagazine.org
symmetrymagazine.org
Physicists like to contract and shorten everything, and while it is fun, you need a dictionary of rules and conventions to write out the full form.
Luckily there are many tricks to use in these shorter representations, but one tends to forget the incredible amount of information within them.
I wrote this just before bed, my estimation skill was already asleep.
Imagine someone opening a pull request with that — it would never pass a code review!
Physics is practiced by hand, pen and paper or chalk and blackboard. There is no IDE or auto-completion.
The short hands, abbreviations, and obscure syntax raise the difficulty to enter into the field but simplify its practice a lot. In fact, it would be nightmarishly verbose if you had to use more explicit terms to the point of making it almost not feasible.
Furthermore, the complexity of learning a few shorthands is incomparable with understanding the underlying concepts. Just because you name things in a more verbose manner and used a more explicit type system you wouldn't be any closer to understanding what any of this means. The effort of learning a short-hand notation to express a concept that takes years of advanced math to grasp is negligible in comparison with the speed up it offers day to day.
The notation is not what is stopping you from understanding it.
"at some point the learning stops and the pain begins"
- S. Rao Kosaraju, Professor Emeritus
Writing it this way goes against the basic idea of QFT, which is that, in a relativistic context, quantum systems can no longer be described as "wave functions evolving in time", which is what the Schrodinger/Hamiltonian formulation describes.
If you're using the non-relativistic approximation, most of the Standard Model is irrelevant since you're limited to interaction energies much less than the rest mass of the lightest particle involved. You're basically looking at the low energy regime of QED, or straightforward non-relativistic QM with an appropriate potential in the Hamiltonian and no pretense of even trying to derive things from an underlying QFT model.
Worse still, practically all such “codes” use shortcuts, simplifications, or outright non-physical spacetimes to reduce the computer power required.
You and I are looking for the same thing, so if you do find a good reference please reply!
The sum is intractable not because it's big but because it can't be sanely approximated by lesser sums, due to the nature of what you're summing - an exponent of i * the integral of the Lagrangian over each spacetime field configuration. This vary likes crazy so if you skip the some parts you might get a completely different result.
The trick to anyhow get anything out of this is to restrict yourself to observables that can be calculated from the ground state, which turn out to be accessible by doing the field integrals over imaginary time instead. This is a trick of calculus, it's not really "non-physical", although it is a pretty crazy method :) This has allowed practitioners to calculate hadron masses for example, it's getting better and better over the decades.
Mathematical formulation of the Standard Model: https://en.wikipedia.org/wiki/Mathematical_formulation_of_th...
"In Gutierrez’s dissemination of the transcript, he noted a sign error he made somewhere in the equation. Good luck finding it!"
In picture form, the full beast looks like: https://upload.wikimedia.org/wikipedia/commons/b/bc/Formula_...