October 5th, 2024

The deconstructed Standard Model equation

The Standard Model of particle physics describes fundamental particles and interactions, using a Lagrangian formulation. It includes gluons, W and Z bosons, and the Higgs boson, with challenges from recent discoveries.

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The deconstructed Standard Model equation

The Standard Model of particle physics is a comprehensive framework that describes the fundamental particles and their interactions. It is often represented as a table, akin to the periodic table, but it is fundamentally a collection of mathematical models. The Lagrangian formulation of the Standard Model is a compact way to express the theory, detailing how particles interact through fundamental forces. The equation includes specific sections dedicated to gluons, W and Z bosons, and the Higgs boson, which are essential for understanding the strong and weak forces. Notably, the model assumes neutrinos are massless, a claim contradicted by recent discoveries. The equation also incorporates virtual particles, referred to as ghosts, to eliminate redundancies in particle interactions. The Faddeev-Popov ghosts specifically address redundancies in weak force interactions. This detailed exploration of the Standard Model highlights its complexity and the ongoing challenges in particle physics, including the need to reconcile the model with new experimental findings.

- The Standard Model is a mathematical framework describing fundamental particles and their interactions.

- The Lagrangian formulation is a compact representation of the Standard Model.

- The model includes sections on gluons, W and Z bosons, and the Higgs boson.

- Recent discoveries challenge the assumption that neutrinos are massless.

- Virtual particles, or ghosts, are used to resolve redundancies in particle interactions.

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By @lnauta - 3 months
What they don't tell you is that if you write out all the indices (mu and nu represent 4 spacetime coordinates, antisymmetric components (f_abc = -f_bac, etc), the kappas and lambdas I don't even remember!), and their contractions [1], this giant equation becomes a few times larger than its current form.

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.

[1] https://en.m.wikipedia.org/wiki/Einstein_notation

By @xpl - 3 months
If treated like code, the expression looks almost grotesquely bad: hundreds of cryptic single-letter variables all over the place, no decomposition, no comments, everything crammed into a monstrous, all-encompassing "god function".

Imagine someone opening a pull request with that — it would never pass a code review!

By @colanderman - 3 months
These field equations I always see presented as the Lagrangian. But I've had trouble locating any presentation of them as field evolution equations (not sure the right term here, but e.g. how Maxwell's equations are typically presented, as partial differential equations with respect to spacetime dimensions). Deriving this form from the Lagrangian seems a daunting and error-prone task. Does anyone know a reference which presents them in this way?
By @qrios - 3 months
The original TeX representation of the formula was written by Thomas D. Gutierrez in 1999 [1]. It was discussed many times on HN, initially in 2016 a day after the post of this article on symmetrymagazine [2].

[1] https://www.tdgutierrez.com/

[2] https://news.ycombinator.com/item?id=12182230

By @readthenotes1 - 3 months
I liked the shade cast on dilettantes in the footnote:

"In Gutierrez’s dissemination of the transcript, he noted a sign error he made somewhere in the equation. Good luck finding it!"

By @akkartik - 3 months
Where's the equality sign? Shouldn't every equation have one?