
The Deconstructed Standard Model Equation - bit-player
http://www.symmetrymagazine.org/article/the-deconstructed-standard-model-equation
======
andrepd
I've been banging my head on QFT and the Standard Model for enough time now
that I can actually glimpse more or less what those terms actualy _mean_ , as
in , I can translate them into words. It's almost like learning a new
language! Pretty awesome.

Still, despite all this complexity, we still have several minor and major
theoretical gaps to fill. Exciting times!

~~~
alanbernstein
I, as a layman with basic college physics knowledge, and passing knowledge of
the standard model, want to understand the meaning of those terms. Do you know
how I can go about that? Ideally, with something a little less dense than a
textbook.

~~~
drauh
I have a PhD in physics, though not particle physics. QFT was required, since
the methods appear all over in condensed matter physics.

Unfortunately, there is no real shortcut to being able to understand those
terms except by studying one of the standard texts. And, physics being what it
is, you can expect a pretty hard slog because the texts will assume you know
first quantization back and forth. Add to that, it's not just QFT but the
domain-specific standard model knowledge.

Dealing with QM requires PDEs, linear algebra, a fair bit of applied analysis
(real and complex). Dealing with QFT requires that, plus learning a bunch of
new techniques with the typical hand-wavy rigor of physics. (Hand-wavy
compared to math.)

If you want to get a feel of the Standard Model without knowing QFT, the text
I used when I took senior-level particle physics is great: Introduction to
Elementa Particles, by David Griffiths. (He's an excellent writer, btw; I
recommend any of his physics books).

As for the standard texts for particle physics, I'm afraid I've been out of
the loop for too long to remember what books were used.

~~~
abecedarius
A related question: Feynman's popular book QED claims to explain quantum
electrodynamics enough that you could almost do calculations with it, just
ridiculously inefficiently. After reading it, I can't: the details left out, I
can't easily fill in from the grad-level texts, even with a pretty decent
undergrad physics background. Shouldn't it be possible to explain QED to a
programmer using a literate program? (Again, an inefficient one.) Was Feynman
exaggerating? Or is it just the tininess of the market of programmers who want
to understand what QED is really about who aren't out to become professional
physicists?

(For others, QED is the part of the standard model about electrons and light
-- the most relevant part for everyday physics and apparently the simplest
part too.)

~~~
namin
Apart the character of physical laws and the easy pieces, what's the gateway
book to understand feynann more advanced work?

~~~
abecedarius
I don't really know, because I don't understand the more advanced work like
QED. But
[http://www.feynmanlectures.caltech.edu/I_toc.html](http://www.feynmanlectures.caltech.edu/I_toc.html)
is one of my favorite books ever.

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dzdt
I would love to see this article, about 5-10 times longer. Dig one level
deeper into what the notation means, how it relates to the zoo of fundamental
particles, etc. Compare and contrast the sections dealing with different
forces/particles. Talk something about the history of how this came out as a
unification of models for gravity, electricity and magnetism, weak force,
strong force.

------
MengerSponge
I love how everybody uses Gutierrez's typesetting. If I ever meet him and have
the presence of mind to put two and two together, I'll buy him a beer.

If you want the TeX source for your own purposes, it's here:
[http://nuclear.ucdavis.edu/~tgutierr/files/stmL1.html](http://nuclear.ucdavis.edu/~tgutierr/files/stmL1.html)

------
hossbeast
What is the sum of terms supposed to be equal to?

~~~
dhoe
It's a Lagrangian, so this is the function nature tries to minimize. In common
everyday systems, the Lagrangian is kinetic energy minus potential energy.

~~~
adrianratnapala
True, but with nitpick that it is the Lagrangian _density_ so nature minimises
its total over a region of 4-space.

And with the more important nitpick that this Lagrangian is a quantum operator
rather than a number. In some sense nature does try to minimise it even so,
but I never got an intuitive grasp on what that sense is.

~~~
cygx
_And with the more important nitpick that this Lagrangian is a quantum
operator rather than a number._

I don't think that's true when dealing with the formulation in terms of path
integrals as we do here...

~~~
adrianratnapala
It's the focus on path integrals that obscures the fact that the Lagrangian is
an operator. Except maybe for convenience, there is nothing about such
equations that is unique to the path-integral formulation.

The fields, the Langragian, and the scattering matrix are all operators; but
of course their matrix elements are numbers. The path-integral formulation is
a good -- and I think physically well motivated -- trick for calculating those
matrix elements in terms of merely fields and their associated Largrangians.

------
nonbel
"To clean up these redundancies, theorists use virtual particles they call
ghosts.

This part of the equation describes how matter particles interact with Higgs
ghosts, virtual artifacts from the Higgs field. [...] This last part of the
equation includes more ghosts. These ones are called Faddeev-Popov ghosts, and
they cancel out redundancies that occur in interactions through the weak
force."

So the second half this equation is used to describe invisible things needed
to cancel out wrong stuff from the first half? Sounds ad hoc to me, were these
"ghosts" predicted by anyone beforehand? Even if not, as a model it can still
be useful though.

~~~
psi-squared
The two types of "ghosts" here are very different. In both cases, though,
they're mathematical artefacts rather than anything "physical", but I'll try
to explain them as well as I know. Disclaimer: The most advanced physics I've
done was a first course in this stuff, so I might be wrong about some things.

For what they're calling "Higgs ghosts": There are two different ways of
describing the electromagnetic and weak forces, and which one is best depends
on how much energy the particles you're dealing with have. At really high
energies, it makes the most sense to talk about a combined "electroweak
force", described in terms of four fields with 2 components each (often called
W1, W2, W3 and B), and one 4-component field (the Higgs field).

In contrast, at low energies, it makes more sense to talk about the
electromagnetic force, with one 2-component field (y), and the weak force,
with three 3-component fields (W+, W-, Z0) and a 1-component field (the Higgs
field, again). So, where did the other three components of the Higgs field go?
Well, we just rearranged things - if you check, the total number of components
stayed the same. There are various names for this rearrangement, and I haven't
seen this one before, but I guess they're calling these "missing" components
"ghosts".

As for the other type, the Faddeev-Popov ghosts, those are more obviously
mathematical artefacts. Normally, you'd start by writing down a "physical"
Lagrangian ("physical" here meaning something like "written in terms of actual
physical fields").

But it turns out that you can't actually calculate with the physical
Lagrangian. So you have to rewrite it in a (mostly) mathematically-equivalent
way, which involves extra fields. These fields come along with extra rules
which basically say "no state you can actually measure involves the ghost
fields in any way". Really, they're just there as a calculational aid and
aren't physically "real", and they're called "ghosts" to reflect that.

Hope that's at least vaguely comprehensible, it's difficult to explain this
stuff without assuming a _lot_ of background knowledge.

~~~
auntienomen
Mostly right, but one correction:

You actually _can_ calculate with the physical Lagrangian. This is what
lattice gauge theory simulations do. But it's inconvenient and difficult in
perturbation theory, so physicists use the Fadeev-Popov ghost trick instead.
The resulting computations are _entirely_ mathematically equivalent, not
"(mostly)".

------
sdenton4
"Note: ...In Gutierrez’s dissemination of the transcript, he noted a sign
error he made somewhere in the equation. Good luck finding it!"

Anyone see the flipped sign?

------
T0T0R0
Given the world we live in, right now, why does mathematics continue to insist
on minified expressions?

Given the option, most development teams would choose to read and write
against verbose source code, rather than scrape obfuscated variables and
method signatures out of a minified, transpiled, compressed package.

So why do we continue this archaic practice of obscure, inscrutable symbols in
mathematics? Cultural inertia?

The cycle of madness must end!

~~~
mirosam
Your comment shows a common misunderstanding of what mathematicians are trying
to do. Modern mathematical notation is not obfuscated, it is in fact making
the object being described much easier to perceive for humans.

Explaining the equation you see in English words is what every physics book
does, however the equation itself represents a concept that is not human. It
comes from an alien universe of symmetries and relations and we have spent
centuries to arrive at the current way of writing these down in a way which
makes them easy to work with.

You can formulate the solution to a quadratic equation as:

The negative linear term, added and subtracted from the square root of the
quantity which is the difference between the square of the linear term and the
product of four times the constant term and the quadratic term, all divided by
twice the quadratic term.

Modern mathematicians write:

x = (-b +- sqrt(b^2 - 4ac)) / 2a

The difference is night and day. You cannot remove the essential complexity
from a problem. You can only try to get close to its representation.

~~~
terryf
While this might not be the OP's point, but for me the main problem are the
one-character variable names. Generally computer code that just operates on
cryptic one-letter variable names, is considered bad code. Yet equations
almost always have one letter variables and the worst part of all, _their
meaning is almost never explained anywhere_

Case in point, what are b, a and c? what is their _meaning_ if I have to
measure them, what is the device for measuring them or what quantity do they
represent?

~~~
orbifold
The point is that variables are evil and arbitrary. So you give them short
names to signal that you could replace them with anything else, what matters
is how they appear together. Additionally different subfields of mathematics
and physics usually adopt naming conventions.

~~~
agumonkey
Took me years before thinking of variables that way and mathematical
expressions are constraints over sets, formulas expressing relations of
interests that way.

------
ars
Am I correct in understanding that this takes every kind of interaction that
particles can have, and simply adds them all together?

How does it deal with some particles only interacting in certain ways and not
others? Is the user of the equation supposed to make sure to enter zero for
those terms, or does the equation capture that knowledge as well?

~~~
sprash
If you apply an operator of such an interaction to the Lagrangian the
equations of motions automatically return zero (e.g. similar to a derivation
of a constant).

------
partycoder
I haven't seen an article so math intensive in a while... since I saw this
one:
[http://www.scholarpedia.org/article/Bayesian_Ying_Yang_learn...](http://www.scholarpedia.org/article/Bayesian_Ying_Yang_learning)

~~~
adrianratnapala
The article displays a big equation somewhat carefully. But it doesn't have
any maths.

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proc0
If I was a physics phd working on QFT, I would tattoo this equation as a
sleeve. Unfortunately, as a mere programmer, I could never pick a sufficiently
perfect code snippet to use. I would constantly look at it and try to refactor
it.

~~~
gosub
[http://blogs.discovermagazine.com/loom/files/2008/07/y-combi...](http://blogs.discovermagazine.com/loom/files/2008/07/y-combinator.jpg)

~~~
proc0
Nice Y combinator lol. Still more math than code.

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lordnacho
There must be some smarter notation that captures the model with less
verbosity?

Also, how on earth did various people put this together? Is there a good book
about it?

~~~
zbyszek
There is; the equation on the CERN mug in the photo is an example. For
example, the gluon Lagrangian (Section 1) may be more compactly written

-1/2 Tr F_{\mu\nu} F^{\mu\nu}

for a suitably defined F. Or further abbreviated to something like L_g.

It just depends on how much detail you need to expose.

------
quirkot
Well, when you put it like that... suddenly it all makes sense :p

Seriously though, very neat to see the actual equation used to model the
universe.

~~~
drauh
When I was a wee undergrad, a grad student office-mate had printed out these
equations and posted them on the office door. He wrote on it: The simplicity
of the Standard Model. Or words to that effect; this was in the condensed
matter physics division.

