some of my neat stuff
git clone git://edryd.org/edryd.org
Log | Files | Refs | LICENSE

commit 21eab252fb1b2ba0829c58f73f74300088750ab3
parent 5b2d01f4173c72298b84e8e6ad71fb3cc38ca734
Author: Ed van Bruggen <edvb@uw.edu>
Date:   Thu, 25 Nov 2021 21:46:17 -0500

Add lattice QCD article

Acontent/posts/lattice-qcd.md | 114+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Alayouts/shortcodes/img.html | 3+++
Astatic/img/posts/lattice-qcd/color.png | 0
Astatic/img/posts/lattice-qcd/fundamental-forces.png | 0
Astatic/img/posts/lattice-qcd/lattice.png | 0
Astatic/img/posts/lattice-qcd/mass-predications.png | 0
Astatic/img/posts/lattice-qcd/more-masses.png | 0
Astatic/img/posts/lattice-qcd/network.png | 0
Astatic/img/posts/lattice-qcd/standard-model.webp | 0
9 files changed, 117 insertions(+), 0 deletions(-)

diff --git a/content/posts/lattice-qcd.md b/content/posts/lattice-qcd.md @@ -0,0 +1,114 @@ +--- +title: "Intro to Lattice Quantum Chromodynamics" +date: 2020-03-20 +tags: physics simulations +categories: phys +--- + +At the start of the 20th century two new revolutionary and counterintuitive areas of +physics were being developed, quantum mechanics and special relativity. While quantum mechanics +describes the strange world of the subatomic with discrete energies, special relativity describes +the effects of moving incredibly fast: time dilation and space contraction (general relativity is +needed for a compete picture with mass warping spacetime). + +In order to understand the dynamics of subatomic particles moving near the speed of light these +two fields had to be united into quantum field theory. This was first done to describe the +electromagnetic force, quantizing it into the theory of quantum electrodynamics (QED) which +satisfies both quantum mechanics and special relativity. However to fully understand the atom, the +strong force also needs to be quantized into quantum chromodynamics (QCD). + +![network](/img/posts/lattice-qcd/network.png) + +The strong force is what overcomes electric repulsion to hold protons and neutrons together +in the nucleus, and binds quarks together to make up the protons and neutrons themselves. As the +name implies, it is extremely strong compared to the electromagnetic force, which is why nuclei +are able to be stable and not fly apart from the protons repelling each other (within certain +limits). + +![fundamental-forces](/img/posts/lattice-qcd/fundamental-forces.png) + +Similar to how the electromagnetic force only interacts with things that have electric charge +(like protons and electrons, not neutrons), the strong force only interacts with things that have +color charge. In the standard model of particle physics, which describes all currently known +particles, the only particles that have color charge are called quarks and gluons. Gluons +mediate the exchange of the strong force, and up and down quarks are what make up protons and +neutrons, being "glued" together by gluons. + +![standard-model](/img/posts/lattice-qcd/standard-model.webp) + +However, unlike electric charge which comes in 2 kinds (positive and negative), color charge +comes in 6 varieties: red, green, and blue, as well as their creatively named opposites anti-red, +anti-green, and anti-blue (sometimes referred to instead as cyan, magenta, and yellow +respectively). While electric charge can be thought of as being on one axis, with negative being +the opposite of positive, color charge has 3 axes, each with its own color and anti-color. +The standard non-antimatter quarks can at anytime have any of the 3 colors, while antimatter +quarks can have any of the 3 anti-colors, and a gluon has one color and one anti-color at all +times. + +When a particle is made up a quark and a anti-quark (called mesons), the anti-quark must have the +anti-color of the quark. Likewise in a particle made up of three quarks (baryons) the quarks must +have different colors, so a proton's up and down quarks must be red, green, and blue, and a +anti-proton must have anti-red, anti-green, and anti-blue anti-quarks. This is due to a concept +called color confinement, quarks can not be observed on their own, and any particle made up of +quarks must have a net zero (also called white) color charge. + +![color](/img/posts/lattice-qcd/color.png) + +Color confinement is one reason why we do not see the strong force play a role in everyday life, +at sizes bigger than a proton it looks like there is no color charge. Another reason is that the +gluon particle has mass unlike the photon which mediates electromagnetism, meaning that it has a +limited lifetime and so can only act on short distances very close to quarks. + +It is also important to note that calling the strong force's charge "color charge" is only an +analogy and visual aid, it has no relation or connection to the physics of color. + +{{<img "https://upload.wikimedia.org/wikipedia/commons/d/d0/Neutron_QCD_Animation.gif" 300 300>}} + +Because of the probabilistic nature of quantum mechanics, to calculate quantum field +theory problems you need to account for all the possible ways an interaction could happen. +This usually entails summing over an infinite number of possible configurations, which is +impossible. Quantum electrodynamics solves this problem using perturbation theory, it can +approximate a calculation by only including the most likely configurations. The more increasingly +less-likely configurations you include the more accurate the calculation is. + +This works in QED because the electromagnetic coupling constant is less than 1, so more +complicated configurations with more interactions contribute less and less to the final answer. +However the strong force's coupling constant is 1, meaning that every possible way an interaction +can happen is equally as likely. This makes it impossible to approximate the most likely +scenarios using this method. + +In order remove this infinity and allow QCD problems to be calculated, space and time are instead +discretized into a finite 4D grid. In this grid each point represents the quark field, and the +lines connecting them represent the gluon field. + +![lattice](/img/posts/lattice-qcd/lattice.png) + +Although this gets around the infinite possible configurations, it is still an extremely large +problem. To reduce the complexity further so it can be computed in a reasonable time a Monte Carlo +algorithm is utilized. Monte Carlo is a method of using random sampling to approximate a problem, +it has many applications to problems in biology (see here for it used for protein folding), +math, and physics. Monte Carlo is best demonstrated as seen below to approximate the value of pi +by seeing if a random point lies within the circle or not, with the more random points the closer +to the true value you get. + +![monte carlo](https://upload.wikimedia.org/wikipedia/commons/8/84/Pi_30K.gif) + +Now with lattice QCD it is possible to preform calculations and make predictions about quarks and +nuclei, such as the mass of mesons and baryons. The graph on the left below shows two different +lattice QCD methods converging to the same mass for a pion, which very closely matches the +experimentally measured mass. However the graph on the right shows what happens when this is +applied to predict the mass of a neutron, they converge to a mass before diverging again. +This divergence is due errors in the Monte Carlo approximation compounding together, creating +a small golden window with the correct mass before error takes over. + +![mass predictions](/img/posts/lattice-qcd/mass-predications.png) + +Lattice QCD can be used to solve countless problems in particle and nuclear physics, such as +the very accurate mass predictions for more hadrons and quarks as seen below. There has also been +a lot of progress in the last 10 years utilizing it to understand QCD decay constants, resonances, +deep inelastic scattering, QCD phase transitions, and investigating color confinement. + +![more masses](/img/posts/lattice-qcd/more-masses.png) + + +This article is based on a presentation I gave in 2020, see the full slides [here](/docs/lattice-qcd.pdf). diff --git a/layouts/shortcodes/img.html b/layouts/shortcodes/img.html @@ -0,0 +1,3 @@ +<div class="col-12 text-center"> + <img src="{{ .Get 0 }}" width="{{ .Get 1 }}" height="{{ .Get 2 }}" class="img-fluid p-md-5"> +</div> diff --git a/static/img/posts/lattice-qcd/color.png b/static/img/posts/lattice-qcd/color.png Binary files differ. diff --git a/static/img/posts/lattice-qcd/fundamental-forces.png b/static/img/posts/lattice-qcd/fundamental-forces.png Binary files differ. diff --git a/static/img/posts/lattice-qcd/lattice.png b/static/img/posts/lattice-qcd/lattice.png Binary files differ. diff --git a/static/img/posts/lattice-qcd/mass-predications.png b/static/img/posts/lattice-qcd/mass-predications.png Binary files differ. diff --git a/static/img/posts/lattice-qcd/more-masses.png b/static/img/posts/lattice-qcd/more-masses.png Binary files differ. diff --git a/static/img/posts/lattice-qcd/network.png b/static/img/posts/lattice-qcd/network.png Binary files differ. diff --git a/static/img/posts/lattice-qcd/standard-model.webp b/static/img/posts/lattice-qcd/standard-model.webp Binary files differ.