As iron sharpens iron, so one person sharpens another Updated 2025-07-16
Proverbs 27:17.
Klein-Gordon equation Updated 2025-07-16
A relativistic version of the Schrödinger equation.
Correctly describes spin 0 particles.
The most memorable version of the equation can be written as shown at Section "Klein-Gordon equation in Einstein notation" with Einstein notation and Planck units:
Has some issues which are solved by the Dirac equation:
- it has a second time derivative of the wave function. Therefore, to solve it we must specify not only the initial value of the wave equation, but also the derivative of the wave equation,As mentioned at Advanced quantum mechanics by Freeman Dyson (1951) and further clarified at: physics.stackexchange.com/questions/340023/cant-the-negative-probabilities-of-klein-gordon-equation-be-avoided, this would lead to negative probabilities.
- the modulus of the wave function is not constant and therefore not always one, and therefore cannot be interpreted as a probability density anymore
- since we are working with the square of the energy, we have both positive and negative value solutions. This is also a features of the Dirac equation however.
Bibliography:
- Video "Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015)" at youtu.be/OCuaBmAzqek?t=600
- An Introduction to QED and QCD by Jeff Forshaw (1997) 1.2 "Relativistic Wave Equations" and 1.4 "The Klein Gordon Equation" gives some key ideas
- 2011 PHYS 485 lecture videos by Roger Moore from the University of Alberta at around 7:30
- www.youtube.com/watch?v=WqoIW85xwoU&list=PL54DF0652B30D99A4&index=65 "L2. The Klein-Gordon Equation" by doctorphys
- sites.ualberta.ca/~gingrich/courses/phys512/node21.html from Advanced quantum mechanics II by Douglas Gingrich (2004)
Quantum field theory bibliography Updated 2025-07-16
Bibliography of the biliograpy:
- physics.stackexchange.com/questions/8441/what-is-a-complete-book-for-introductory-quantum-field-theory "What is a complete book for introductory quantum field theory?"
- www.quora.com/What-is-the-best-book-to-learn-quantum-field-theory-on-your-own on Quora
- www.amazon.co.uk/Lectures-Quantum-Field-Theory-Ashok-ebook/dp/B07CL8Y3KY
Recommendations by friend P. C.:
- The Global Approach to Quantum Field Theory
- Lecture Notes | Geometry and Quantum Field Theory | Mathematics ocw.mit.edu/courses/mathematics/18-238-geometry-and-quantum-field-theory-fall-2002/lecture-notes/
- Towards the mathematics of quantum field theory (Frederic Paugam)
- Path Integrals in Quantum Mechanics (J. Zinn–Justin)
- (B.Hall) Quantum Theory for Mathematicians (B.Hall)
- Quantum Field Theory and the Standard Model (Schwartz)
- The Algebra of Grand Unified Theories (John C. Baez)
- quantum Field Theory for The Gifted Amateur by Tom Lancaster (2015)
Aspen HYSYS Updated 2025-07-16
Aspen Hysys Introduction by Emmanuel Oloyede (2016)
Source. Holy crap, the UI is identical to Microsoft Word with that huge top bar!!! Associative array Updated 2025-07-16
Quantum field theory book Updated 2025-07-16
- web.archive.org/web/20150623011722/http://users.physik.fu-berlin.de/~kleinert/b6/psfiles/qft.pdf by Hagen Kleinert (2015). 1500 pages!
- The Quantum Theory of Fields by Steven Weinberg (2013) www.cambridge.org/core/books/quantum-theory-of-fields/22986119910BF6A2EFE42684801A3BDF
- Quantum Field Theory by Lewis H. Ryder 2nd edition (1996) www.amazon.co.uk/Quantum-Field-Theory-Lewis-Ryder/dp/0521478146
- Lectures of Quantum Field Theory by Ashok Das (2018) www.amazon.co.uk/Lectures-Quantum-Field-Theory-Ashok-ebook/dp/B07CL8Y3KY
- A Modern Introduction to Quantum Field Theory by Michele Maggiore (2005) www.amazon.co.uk/Modern-Introduction-Quantum-Theory-Physics/dp/0198520743
Quantum Field Theory book by Mark Srednicki (2006) Updated 2025-07-16
Free to view draft: web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf Page presenting it: web.physics.ucsb.edu/~mark/qft.html
Number of pages: 616!
Don't redistribute clause, and final version by Cambridge University Press, alas, so corrections will never be merged back: web.physics.ucsb.edu/~mark/qft.html. But at least he's collecing erratas for the published (and therefore draft) versions there.
The preface states that one of its pedagogical philosophies is to "Illustration of the basic concepts with the simplest examples.", so maybe there is hope after all.
Asterism (astronomy) Updated 2025-07-16
Basically a mini-Constellation.
Carl Jung Updated 2025-07-16
bgrep Updated 2025-07-16 Biathlon Updated 2025-07-16
Cartesius (1974) Updated 2025-07-16
Quantum Intermediate Representation Updated 2025-07-16
Presumably the point of it is to allow simulation in classical computers?
Cavendish Laboratory Updated 2025-07-16
Cayley-Dickson construction Updated 2025-07-16
Constructs the quaternions from complex numbers, octonions from quaternions, and keeps doubling like this indefinitely.
Cheap robot Updated 2025-07-16
Quantum key distribution Updated 2025-07-16
Man-in-the-middle attack
quantumcomputing.stackexchange.com/questions/142/advantage-of-quantum-key-distribution-over-post-quantum-cryptography/25727#25727 Advantage of quantum key distribution over post-quantum cryptography has Ciro Santilli's comparison to classical encryption.
Long story short:
- QKD allows you to generate shared keys without public-key cryptography. You can then use thses shared keys
- QKD requires authentication on a classical channel, exactly like a classical public-key cryptography forward secrecy would. The simplest way to do this is a with a pre-shared key, just like in classical public key cryptography. If that key is compromised at any point, your future messages can get man-in-the-middle'd, exactly like in classical cryptography.
QKD uses quantum mechanics stuff to allow sharing unsnoopable keys: you can detect any snooping and abort communication. Unsnoopability is guaranteed by the known laws of physics, up only to engineering imperfections.
Furthermore, it allows this key distribution without having to physically take a box by car somewhere: once the channel is established, e.g. optical fiber, you can just keep generating perfect keys from it. Otherwise it would be pointless, as you could just drive your one-time pad key every time.
However, the keys likely have a limited rate of generation, so you can't just one-time pad the entire message, except for small text messages. What you would then do is to use the shared key with symmetric encryption.
Therefore, this setup usually ultimately relies on the idea that we believe that symmetric encryption is safer than , even though there aren't mathematical safety proofs of either as of 2020.
Quantum mechanics Updated 2025-07-16
Quantum mechanics is quite a broad term. Perhaps it is best to start approaching it from the division into:
- non-relativistic quantum mechanics: obviously the simpler one, and where you should start
- relativistic quantum mechanics: more advanced, and arguably "less useful"
Key experiments that could not work without quantum mechanics: Section "Quantum mechanics experiment".
Mathematics: there are a few models of increasing precision which could all be called "quantum mechanics":
Ciro Santilli feels that the largest technological revolutions since the 1950's have been quantum related, and will continue to be for a while, from deeper understanding of chemistry and materials to quantum computing, understanding and controlling quantum systems is where the most interesting frontier of technology lies.
Chicago Updated 2025-07-16
Chorus effect Updated 2025-07-16
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