Mathematical formulation of quantum field theory Updated 2025-07-16
The Dirac equation, OK, is a partial differential equation, so we can easily understand its definition with basic calculus. We may not be able to solve it efficiently, but at least we understand it.
But what the heck is the mathematical model for a quantum field theory? TODO someone was saying it is equivalent to an infinite set of PDEs somehow. Investigate. Related:
The path integral formulation might actually be the most understandable formulation, as shown at Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979).
Quantum electrodynamics by Lifshitz et al. 2nd edition (1982) chapter 1. "The uncertainty principle in the relativistic case" contains an interesting idea:
The foregoing discussion suggests that the theory will not consider the time dependence of particle interaction processes. It will show that in these processes there are no characteristics precisely definable (even within the usual limitations of quantum mechanics); the description of such a process as occurring in the course of time is therefore just as unreal as the classical paths are in non-relativistic quantum mechanics. The only observable quantities are the properties (momenta,
polarizations) of free particles: the initial particles which come into interaction, and the final particles which result from the process.
Mathematician Updated 2025-07-16
Poet, scientists and warriors all in one? Conquerors of the useless.
A wise teacher from University of São Paulo once told the class Ciro Santilli attended an anecdote about his life:It turned out that, about 10 years later, Ciro ended up following this advice, unwittingly.
I used to want to learn Mathematics.But it was very hard.So in the end, I became an engineer, and found an engineering solution to the problem, and married a Mathematician instead.
Mathematics Updated 2025-07-16
The proper precise definition of mathematics can be found at: Section "Formalization of mathematics".
The most beautiful things in mathematics are described at: Section "The beauty of mathematics".
Study Hilbert spaces desert dilemma meme
. Source. Applies to almost all of mathematics of course. But we don't care, do we! Ciro Santilli's e-soulmates Updated 2025-07-16
These are people which Ciro never met personally, and who might not know that Ciro exists, or might never had any direct 1-2-1 online contact with Ciro, but Ciro is convinced are his brothers in some other dimension due to how many opinions or behaviours he feels they share:
- Dan Dascalescu due to articles such as:
- English as a universal language by Dan Dascalescu (2008)
- www.reddit.com/r/TheoryOfReddit/comments/9oujwf/why_archiving_old_threads_is_a_bigger_problem/ see also online forums that lock threads after some time are evil
- web.archive.org/web/20130922192354/http://wiki.dandascalescu.com/reviews/online_services/web_page_archiving see also web archiving
- random posts on OpenStreetMap, and about China: help.openstreetmap.org/questions/29300/legality-status-of-mapping-activity-in-china?page=1&focusedAnswerId=42167#42167
- kenorb see also Ciro Santilli's Stack Overflow contributions
- Gwern Branwen
Ciro sometimes ponders why is it so hard to find people online that you truly love and admire. Maybe it is for similar reasons why it is also hard in the real world: the great variety of human interest, and the great limitation of our attention spans. But online, where we have access to "everyone", shouldn't it should be easier? Not naturally finding such people is perhaps one of the greatest failings of our education system.
Ciro Santilli's fetishes Updated 2025-07-16
Ciro Santilli's film tastes Updated 2025-07-16
Ciro Santilli has already watched all the best films in history, and as a result any of those new movies that is full of clichés and has no innovative aspect at all (99.99999% of all modern movies) makes Ciro want to puke and to start Googling TV Tropes to classify as many clichés as possible.
Good movies are those that teach you mechanisms of the real world. Willing suspension of disbelief must be maintained at all costs.
Love is not an interesting aspect of the world. You solve your love life at university, Tinder or Tango.
The actually interesting aspects of the world are:
The Sliding scale of idealism vs. cynicism must be close to Cynicism max at all times. Movies with pure good and pure bad are shit.
Matplotlib Updated 2025-07-16
Tends to be Ciro's pick if gnuplot can't handle the use case, or if the project is really really serious.
Couldn't handle exploration of large datasets though: Survey of open source interactive plotting software with a 10 million point scatter plot benchmark by Ciro Santilli
Examples:
- matplotlib/hello.py
- matplotlib/educational2d.py
- matplotlib/axis.py
- matplotlib/label.py
- Line style
- Subplots
- matplotlib/two_lines.py
- Data from files
- Specialized
Matrix mechanics Updated 2025-07-16
Published by Werner Heisenberg in 1925-07-25 as quantum mechanical re-interpretation of kinematic and mechanical relations by Heisenberg (1925), it offered the first general formulation of quantum mechanics.
It is apparently more closely related to the ladder operator method, which is a more algebraic than the more analytical Schrödinger equation.
It appears that this formulation makes the importance of the Poisson bracket clear, and explains why physicists are so obsessed with talking about position and momentum space. This point of view also apparently makes it clearer that quantum mechanics can be seen as a generalization of classical mechanics through the Hamiltonian.
QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) mentions however that relativistic quantum mechanics broke that analogy, because some 2x2 matrix had a different form, TODO find that again.
Inward Bound by Abraham Pais (1988) chapter 12 "Quantum mechanics, an essay" part (c) "A chronology" has some ultra brief, but worthwhile mentions of matrix mechanics and the commutator.
Matrix representation of a bilinear form Updated 2025-07-16
As usual, it is useful to think about how a bilinear form looks like in terms of vectors and matrices.
Unlike a linear form, which was a vector, because it has two inputs, the bilinear form is represented by a matrix which encodes the value for each possible pair of basis vectors.
Matrix ring Updated 2025-07-16
The matrix ring of degree n is the set of all n-by-n square matrices together with the usual vector space and matrix multiplication operations.
Maxwell-Boltzmann distribution Updated 2025-07-16
Maxwell-Boltzmann distribution for three different temperatures
. Reduction of an elliptic curve over the rational numbers to an elliptic curve over a finite field mod p Updated 2025-07-16
This construction takes as input:and it produces an elliptic curve over a finite field of order as output.
The constructions is used in the Birch and Swinnerton-Dyer conjecture.
To do it, we just convert the coefficients and from the Equation "Definition of the elliptic curves" from rational numbers to elements of the finite field.
For the denominator , we just use the multiplicative inverse, e.g. supposing we havewhere because , related: math.stackexchange.com/questions/1204034/elliptic-curve-reduction-modulo-p
Ciro Santilli's hardware External storage Updated 2025-07-16
Ciro Santilli's hardware Google Pixel 3a (2020) Updated 2025-07-16
Bought: January 2020 from store.google.com/ for 350 pounds.
GMS Arena: www.gsmarena.com/google_pixel_3a-9408.php
Front camera video on Android 11: about 100MiB / minute. The encoding is however super inefficient, a FFmpeg re-encode without any options reduces it by 1/3.
For Fastboot mode: Power and Volume down simultaneously for 10-15s. It is OK if screen sleeps. On "no command", power then volume up to see options.
2023-10: touchscreen not registering touches anymore. Still displays images. Manage to regain access with wired USB mouse + a simple USB-C adapter. RIP. Will attempt replacement: store.ifixit.co.uk/products/google-pixel-3a-screen-genuine?variant=42388954448071, partly to get Authy access which I had never properly tested... Replaced screen, but at exact same status as before: shows image but no touch. thus I wasted my money and time (minus the learning) something else is broken.
Hide top bar on Ubuntu Updated 2025-07-16
Or likely more generally, on GNOME desktop, which is the default desktop environment as of Ubuntu 22.10.
High flying bird vs gophers Updated 2025-07-16
Ciro once read that there are two types of mathematicians/scientists (he thinks it was comparing Einstein to some Jack of all trades polymath who didn't do any new discoveries):
- high flying birds, who know a bit of everything, feel the beauty of each field, but never dig deep in any of them
- gophers, who dig all the way down, on a single subject, until they either get the Nobel Prize, or work on the wrong problem and waste their lives
TODO long after Ciro forgot where he had read this from originally, someone later pointed him to: www.ams.org/notices/200902/rtx090200212p.pdf Birds and Frogs by Freeman Dyson (2009), which is analogous but about Birds and Frogs. So did Ciro's memory play a trick on him, or is there also a variant; of this metaphor with a gopher?
Ciro is without a doubt the bird type. Perhaps the ultimate scientist is the one who can combine both aspects in the right amount?
Ciro gets bored of things very quickly.
Once he understands the general principles, if the thing is not the next big thing, Ciro considers himself satisfied without all the nitty gritty detail, and moves on to the next attempt.
In the field of mathematics for example, Ciro is generally content with understanding cool theorem statements. More generally, one of Ciro's desires is for example to understand the significance of each physics Nobel Prize.
This is also very clear for example after Ciro achieved Linux Kernel Module Cheat: he now had the perfect setup to learn all the Linux kernel shady details but at the same time after all those years he finally felt that "he could do it, so that was enough", and soon moved to other projects.
If Ciro had become a scientist, he would write the best review papers ever, just like in the current reality he writes amazing programming tutorials on Stack Overflow.
Ciro has in his mind an overly large list of subjects that "he feels he should know the basics of", and whenever he finds something in one of those topics that he does not know enough about, he uncontrollably learns it, even if it is not the most urgent thing to be done. Or at least he puts a mention on his "list of sources" about the subject. Maybe everyone is like that. But Ciro feels that he feels this urge particularly strongly. Correspondingly, if a subject is not in that list, Ciro ignores it without thinking twice.
Ciro believes that high flying birds are the type of people better suited for venture capital investment management: you know a bit of what is hot on several fields to enough depth to decide where to place your bets and how to guide them. But you don't have the patience to actually go deeply into any one of them and deal with each individual shit that comes up.
Cosmos: A Personal Voyage (1980) episode 1 mentions as quoted by the Wikipedia page for Eratosthenes:That's Ciro.
According to an entry in the Suda (a 10th-century encyclopedia), his critics scorned him, calling him beta (the second letter of the Greek alphabet) because he always came in second in all his endeavors.
Ciro Santilli's hardware House 2018-01 Aluminium extractor filter Updated 2025-07-16
This is the exact model: shop.elica.com/en/accessori/filtro-grassi-in-alluminio-cod-gf03fc.html | web.archive.org/web/20190707053526/https://shop.elica.com/en/accessori/filtro-grassi-in-alluminio-cod-gf03fc.html
Searching by th epart name "GF03FC" leads to other sellers besides Elica however, which could reduce shipping costs: www.cookerhoodsupplies.co.uk/filters-and-lamps/188-metal-grease-filter-gf03fc.html
Brand on filter itself: "ARMA Filtre a.s." based on markings: www.armafiltre.com.tr/uygulamalar/7/3/en/Home-Appliances.html Cannot find any model on website however... looks like Elica's B2B supplier only.
July 2019 message:
Aluminium extractor filter for 208298104403Hi there,I'm trying to buy a spare aluminium extractor filter for an Elica extractor, but I can't find the right size on the website.My 12NC is : 208298104403My filter looks a lot like this: shop.elica.com/en/accessori/filtro-grassi-in-alluminio-cod-GRI0077330A.html but the dimensions are different: I measured 45.9cm x 17.6cm on my old one.Do you have that for sale?
Ciro Santilli's hardware House 2018-01 Fire alarms Updated 2025-07-16
Kitchen: 2021-04: nine-volt battery battery at 8.79V. Not sounding.
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