The number 197 is an integer that comes after 196 and before 198. It is an odd number and has several interesting properties: 1. **Prime Number**: 197 is a prime number, meaning it is greater than 1 and has no positive divisors other than 1 and itself. 2. **Numerical Properties**: It is a three-digit number written as 197 in decimal notation.
Mathematical formulation of quantum field theory by 
Ciro Santilli 37 Updated 2025-06-17 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-06-17 +Created 1970-01-01The 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.
The 1942 Herefordshire TRE (Telecommunications Research Establishment) Halifax crash refers to an incident involving a British Royal Air Force (RAF) aircraft, specifically a Handley Page Halifax bomber, that crashed in Herefordshire, England during World War II. On 23rd December 1942, the Halifax Bomber V9977 was on a test flight when it encountered difficulties and subsequently crashed near the village of Llangarron.
Initially a phenomenological guess to explain the periodic table. Later it was apparently proven properly with the spin-statistics theorem, physics.stackexchange.com/questions/360140/theoretical-proof-of-paulis-exclusion-principle.
And it was understood more and more that basically this is what prevents solids from collapsing into a single nucleus, not electrical repulsion: electron degeneracy pressure!
Bibliography:
- www.youtube.com/watch?v=EK_6OzZAh5k How Electron Spin Makes Matter Possible by PBS Space Time (2021)
A "singing candle" refers to a type of decorative candle that emits sound, often music or melodies, as it burns. These candles are typically designed with a small electronic component or speaker incorporated into them, allowing them to play tunes when lit. The concept combines visual ambiance with auditory enjoyment, making them popular for special occasions like birthdays, celebrations, or as unique home decor.
Robert McCann is a prominent mathematician known for his work in the fields of partial differential equations, geometric analysis, and optimal transport. He is a professor at the University of Toronto and has made significant contributions to the mathematical understanding of transport phenomena, which has applications in various areas such as economics, fluid dynamics, and more. One of his notable achievements is the application of optimal transport theory to problems in differential geometry and the study of Ricci flow.
The 18th meridian west is a line of longitude that is 18 degrees west of the Prime Meridian, which is located at 0 degrees longitude. This meridian runs from the North Pole to the South Pole and passes through several countries and bodies of water. In Europe, the 18th meridian west crosses parts of Norway (specifically the island of Svalbard), and it further passes through Greenland.
The 1872 Baltic Sea flood, also known as the Great Flood of 1872, was a significant and catastrophic weather event that affected the coastal regions around the Baltic Sea, particularly impacting areas in what is now Germany, Poland, and parts of the Scandinavian countries. The flood occurred during the night of October 30 to October 31, 1872, following a combination of heavy rainfall and strong winds, which led to a rapid rise in water levels.
Plane-wave expansion is a mathematical method used primarily in the fields of electromagnetics, optics, and solid-state physics to represent a complex wave function or field in terms of a sum of plane waves. This technique is particularly useful for analyzing wave behavior, diffraction, and propagation in periodic structures, such as photonic crystals or quantum wells.
The 176th meridian west is a line of longitude that is located 176 degrees west of the Prime Meridian, which runs through Greenwich, England. This meridian passes through the Pacific Ocean and is notable for being close to the International Date Line, which is approximately at 180 degrees longitude. The area around the 176th meridian west includes various islands, such as parts of the Aleutian Islands in Alaska and other territories in the Pacific.
The Larch family, scientifically known as **Pinaceae**, is a family of coniferous trees and shrubs. The family includes various genera and species, among which the genus **Larix**, commonly referred to as larch, is notable. Larches are unique among conifers because they are deciduous, meaning they lose their needles in the fall, unlike many other conifer species that retain their foliage year-round.
The 172nd meridian east is an imaginary line of longitude that is 172 degrees east of the Prime Meridian, which is located at 0 degrees longitude. This meridian runs vertically from the North Pole to the South Pole and is used for navigation and geographic reference. Geographically, the 172nd meridian east passes through several regions, including parts of the Pacific Ocean and various islands.
The term "16th-century Greek physicists" may refer to scientists and philosophers of Greek heritage who were active during the 16th century, a period that was marked by significant advancements in science and a revival of ancient knowledge, particularly due to the Renaissance. However, it's important to note that the term may not directly correspond to a specific group of physicists in the way that we think of them today.
The 168th meridian west is a line of longitude located 168 degrees west of the Prime Meridian, which is at 0 degrees longitude. It runs from the North Pole to the South Pole, passing through the Pacific Ocean, and it is primarily located in the ocean with very few land areas directly intersecting it. In terms of geography, the 168th meridian west lies just to the east of the International Date Line, which is generally around 180 degrees longitude.
Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact