Ciro Santilli @cirosantilli 37

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Einstein notation Updated 2025-07-16

The Wikipedia page of this article is basically a masterclass why Wikipedia is useless for learning technical subjects. They are not even able to teach such a simple subject properly there!

Bibliography:

www.maths.cam.ac.uk/postgrad/part-iii/files/misc/index-notation.pdf gives a definition that does not consider upper and lower indexes, it only counts how many times the indices appear
Their definition of the Laplacian is a bit wrong as only one $i$ appears in it, they likely meant to have written $\frac{\partial}{\partial x _{i}} \frac{\partial F}{\partial x _{i}}$ instead of $\frac{\partial ^{2} F}{\partial x _{i}^{2}}$ , related:

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Electric guitar Updated 2025-07-16

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See also some remarks of Ciro Santilli's thoughts on the instrument Ciro Santilli's musical education.

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Electromagnetic induction Updated 2025-07-16

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Electron gas Updated 2025-07-16

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Partial label partial derivative notation Updated 2025-07-16

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Royal Society Updated 2025-07-16

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They do two things:

make a closed source science journal with insanely high impact factor as of 2019
gamify science by letting (mostly mostly British) dudes like Newton and Paul Dirac add some random letters after their real names to show off

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Song dynasty Updated 2025-07-16

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TeachMeAsap.com Updated 2025-07-16

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They sent one of the rare spams Ciro actually was interested in!!! Likely going down lists of top Stack Overflow users.

They have some kind of cryptocurrency, TCHME token, as a reward. Ciro wonders if the value of TCHME will ever be high enough to serve as a valid incentive.

Also, what is the total TCHME supply? Can the website devs issue as much as they want? They do giveaways e.g. as shown at: twitter.com/TeachMeAsap/status/1621353671840899072

And a centralized system with a certralized marketplace would work just as well for the initial phases. But fair play, the idea is interesting.

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Test data 7 Updated 2025-07-16

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Twin prime Updated 2025-07-16

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Order of a tensor Updated 2025-07-16

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T^{(m, n)}

has order

(m, n)

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Partial index partial derivative notation Updated 2025-07-16

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This notation is not so common in basic mathematics, but it is so incredibly convenient, especially with Einstein notation as shown at Section "Einstein notation for partial derivatives":

\partial_{0} F (x, y, z) = \frac{\partial F ( x , y , z )}{\partial x} \partial_{1} F (x, y, z) = \frac{\partial F ( x , y , z )}{\partial y} \partial_{2} F (x, y, z) = \frac{\partial F ( x , y , z )}{\partial x}

(1)

This notation is similar to partial label partial derivative notation, but it uses indices instead of labels such as

x

y

, etc.

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Quantum Field Theory lecture notes by David Tong (2007) Updated 2025-07-16

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www.damtp.cam.ac.uk/user/tong/qft/qft.pdf

Author: David Tong.

Number of pages circa 2021: 155.

It should also be noted that those notes are still being updated circa 2020 much after original publication. But without Git to track the LaTeX, it is hard to be sure how much. We'll get there one day, one day.

Likely used at: David Tong's 2009 Quantum Field Theory lectures at the Perimeter Institute.

Some quotes self describing the work:

an Introduction To Quantum Field Theory by Peskin and Schroeder (1995)
This is a very clear and comprehensive book, covering everything in this course at the right level. To a large extent, our course will follow the first section of this book.
Perhaps for this reason Ciro Santilli was not able to get as much as he'd out of those notes either. This is not to say that the notes are bad, just not what Ciro needed, much like P&S:
- the missing link between basic and advanced
- doing physics means calculating a number
In this course we will not discuss path integral methods, and focus instead on canonical quantization.