Like the rest of the Standard Model Lagrangian, this can be split into two parts:
- spacetime symmetry: reaches the derivation of the Dirac equation, but has no interactions
- add the internal symmetry to add interactions, which reaches the full equation
Deriving the qED Lagrangian by Dietterich Labs (2018)
Source. As mentioned at the start of the video, he starts with the Dirac equation Lagrangian derived in a previous video. It has nothing to do with electromagnetism specifically.
He notes that that Dirac Lagrangian, besides being globally Lorentz invariant, it also also has a global invariance.
However, it does not have a local invariance if the transformation depends on the point in spacetime.
He doesn't mention it, but I think this is highly desirable, because in general local symmetries of the Lagrangian imply conserved currents, and in this case we want conservation of charges.
To fix that, he adds an extra gauge field (a field of matrices) to the regular derivative, and the resulting derivative has a fancy name: the covariant derivative.
Then finally he notes that this gauge field he had to add has to transform exactly like the electromagnetic four-potential!
So he uses that as the gauge, and also adds in the Maxwell Lagrangian in the same go. It is kind of a guess, but it is a natural guess, and it turns out to be correct.
Electroweak Theory and the Origin of the Fundamental Forces by PBS Space Time (2020)
Source. Unsatisfactory, as usual.
Somewhat midway between a syllabary and an alphabet: you write out consonants, and vowels are "punctuation-like-modifiers".
Array of
Elf64_Shdr structs.Each entry contains metadata about a given section.
e_shoff of the ELF header gives the starting position, 0x40 here.So the table takes bytes from 0x40 to
0x40 + 7 + 0x40 - 1 = 0x1FF.Some section names are reserved for certain section types: www.sco.com/developers/gabi/2003-12-17/ch4.sheader.html#special_sections e.g.
.text requires a SHT_PROGBITS type and SHF_ALLOC + SHF_EXECINSTRRunning:outputs:
readelf -S hello_world.oThere are 7 section headers, starting at offset 0x40:
Section Headers:
[Nr] Name Type Address Offset
Size EntSize Flags Link Info Align
[ 0] NULL 0000000000000000 00000000
0000000000000000 0000000000000000 0 0 0
[ 1] .data PROGBITS 0000000000000000 00000200
000000000000000d 0000000000000000 WA 0 0 4
[ 2] .text PROGBITS 0000000000000000 00000210
0000000000000027 0000000000000000 AX 0 0 16
[ 3] .shstrtab STRTAB 0000000000000000 00000240
0000000000000032 0000000000000000 0 0 1
[ 4] .symtab SYMTAB 0000000000000000 00000280
00000000000000a8 0000000000000018 5 6 4
[ 5] .strtab STRTAB 0000000000000000 00000330
0000000000000034 0000000000000000 0 0 1
[ 6] .rela.text RELA 0000000000000000 00000370
0000000000000018 0000000000000018 4 2 4
Key to Flags:
W (write), A (alloc), X (execute), M (merge), S (strings), l (large)
I (info), L (link order), G (group), T (TLS), E (exclude), x (unknown)
O (extra OS processing required) o (OS specific), p (processor specific)The
struct represented by each entry is:typedef struct {
Elf64_Word sh_name;
Elf64_Word sh_type;
Elf64_Xword sh_flags;
Elf64_Addr sh_addr;
Elf64_Off sh_offset;
Elf64_Xword sh_size;
Elf64_Word sh_link;
Elf64_Word sh_info;
Elf64_Xword sh_addralign;
Elf64_Xword sh_entsize;
} Elf64_Shdr;
A rigid body is a solid object in which the distance between any two points within the object remains constant regardless of external forces or moments acting on it. In other words, a rigid body does not deform under the influence of forces; it maintains its shape and size. Key characteristics of a rigid body include: 1. **Invariance of Shape and Size**: The distances between points within the body do not change.
Pinned article: 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