Palm calculus is a mathematical framework used primarily in the fields of stochastic processes and queueing theory, particularly for analyzing systems involving random points in time or space, such as arrival processes. It is named after the Swedish mathematician Gunnar Palm, who contributed to the development of this theory.

Unified Modeling Language (UML) is a standardized modeling language used in software engineering to visualize, specify, construct, and document the artifacts of a software system. The applications of UML are broad and can be categorized into several areas: 1. **Software Design and Architecture**: - **Object-Oriented Design**: UML helps in designing software systems using object-oriented principles. Class diagrams, component diagrams, and package diagrams are used to represent the structure of a system.

David Harel is a prominent computer scientist known for his contributions to several areas in computer science, particularly in theoretical computer science, software engineering, and the design of programming languages. He is best known for his work on state machines, model checking, and formal methods. One of Harel's key contributions is the development of the Harel State Chart technique, which extends Finite State Machines and is widely used for modeling complex systems.

An inner class in Java is a class that is defined within the body of another class. It has access to the members (fields and methods) of the outer class, even if they are declared private. Inner classes can be used to logically group classes that are only used in one place, increasing the encapsulation and readability of the code. There are four types of inner classes in Java: 1. **Non-static Inner Class**: These are tied to an instance of the outer class.

PlantUML is an open-source tool used to create diagrams from plain text descriptions. It enables users to generate a variety of UML (Unified Modeling Language) diagrams, including class diagrams, sequence diagrams, use case diagrams, activity diagrams, component diagrams, state diagrams, and more. PlantUML's syntax is designed to be simple and intuitive, allowing users to write textual representations of diagrams that can then be rendered into graphical formats, such as PNG, SVG, or PDF.

A use case diagram is a visual representation of the interactions between users (or "actors") and a system to achieve specific goals. It is commonly used in software engineering and system design to help stakeholders understand the functional requirements of a system. Use case diagrams are part of the Unified Modeling Language (UML), which is a standardized modeling language in software engineering.

The Majorana equation is a relativistic wave equation that describes particles known as Majorana fermions. These particles are unique in that they are their own antiparticles, meaning that they possess the same quantum numbers as their antiparticles, unlike traditional fermions (like electrons), which have distinct antiparticles (such as positrons).

C-symmetry, also known as charge conjugation symmetry, refers to a fundamental symmetry in particle physics concerning the transformation of particles into their corresponding antiparticles. Specifically, it involves changing a particle into its antiparticle, which has the opposite electric charge and other quantum numbers. In terms of mathematical representation, charge conjugation transforms a particle state \(| \psi \rangle\) into its charge-conjugated state \(| \psi^C \rangle\).

Yup, this one Focks you up.

Second quantization also appears to be useful not only for relativistic quantum mechanics, but also for condensed matter physics. The reason is that the basis idea is to use the number occupation basis. This basis is:

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Basically a synonym for second quantization.

Thought experiment that illustrates the path integral formulation of quantum field theory.

Mentioned for example in quantum field theory in a nutshell by Anthony Zee (2010) page 8.

www.youtube.com/watch?v=WB8r7CU7clk&list=PLUl4u3cNGP60TvpbO5toEWC8y8w51dtvm by Iain Stewart. Basically starts by explaining how quantum field theory is so generic that it is hard to get any numerical results out of it :-)

But in particular, we want to describe those subtheories in a way that we can reach arbitrary precision of the full theory if desired.

Theory that describes electrons and photons really well, and as Feynman puts it "accounts very precisely for all physical phenomena we have ever observed, except for gravity and nuclear physics" ("including the laughter of the crowd" ;-)).

Learning it is one of Ciro Santilli's main intellectual fetishes.

While Ciro acknowledges that QED is intrinsically challenging due to the wide range or requirements (quantum mechanics, special relativity and electromagnetism), Ciro feels that there is a glaring gap in this moneyless market for a learning material that follows the Middle Way as mentioned at: the missing link between basic and advanced. Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) is one of the best attempts so far, but it falls a bit too close to the superficial side of things, if only Feynman hadn't assumed that the audience doesn't know any mathematics...

The funny thing is that when Ciro Santilli's mother retired, learning it (or as she put it: "how photons and electrons interact") was also one of her retirement plans. She is a pharmacist by training, and doesn't know much mathematics, and her English was somewhat limited. Oh, she also wanted to learn how photosynthesis works (possibly not fully understood by science as that time, 2020). Ambitious old lady!!!

Experiments: quantum electrodynamics experiments.

Combines special relativity with more classical quantum mechanics, but further generalizing the Dirac equation, which also does that: Dirac equation vs quantum electrodynamics. The name "relativistic" likely doesn't need to appear on the title of QED because Maxwell's equations require special relativity, so just having "electro-" in the title is enough.

Before QED, the most advanced theory was that of the Dirac equation, which was already relativistic but TODO what was missing there exactly?

As summarized at: youtube.com/watch?v=_AZdvtf6hPU?t=305 Quantum Field Theory lecture at the African Summer Theory Institute 1 of 4 by Anthony Zee (2004):

That video also mentions the interesting idea that:Therefore, for small timescales, energy can vary a lot. But mass is equivalent to energy. Therefore, for small time scale, particles can appear and disappear wildly.

QED is the first quantum field theory fully developed. That framework was later extended to also include the weak interaction and strong interaction. As a result, it is perhaps easier to just Google for "Quantum Field Theory" if you want to learn QED, since QFT is more general and has more resources available generally.

Like in more general quantum field theory, there is on field for each particle type. In quantum field theory, there are only two fields to worry about:

Experiments explained by QED but not by the Dirac equation:

2s/2p energy split in the hydrogen emission spectrum, not predicted by the Dirac equation, but explained by quantum electrodynamics, which is one of the first great triumphs of that theory.

Note that for atoms with multiple electrons, 2s/2p shifts are expected: Why does 2s have less energy than 1s if they have the same principal quantum number?. The surprise was observing that on hydrogen which only has one electron.

Initial experiment: Lamb-Retherford experiment.

On the return from the train from the Shelter Island Conference in New York, Hans Bethe managed to do a non-relativistic calculation of the Lamb shift. He then published as The Electromagnetic Shift of Energy Levels by Hans Bethe (1947) which is still paywalled as of 2021, fuck me: journals.aps.org/pr/abstract/10.1103/PhysRev.72.339 by Physical Review.

The Electromagnetic Shift of Energy Levels Freeman Dyson (1948) published on Physical Review is apparently a relativistic analysis of the same: journals.aps.org/pr/abstract/10.1103/PhysRev.73.617 also paywalled as of 2021.

TODO how do the infinities show up, and how did people solve them?

www.mdpi.com/2624-8174/2/2/8/pdf History and Some Aspects of the Lamb Shift by G. Jordan Maclay (2019)

Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) mentions it several times.

This was one of the first two great successes of quantum electrodynamics, the other one being the Lamb shift.

In youtu.be/UKbp85zpdcY?t=52 from freeman Dyson Web of Stories interview (1998) Dyson mentions that the original key experiment was from Kusch and Foley from Columbia University, and that in 1948, Julian Schwinger reached the correct value from his calculations.

Apparently first published at The Magnetic Moment of the Electron by Kusch and Foley (1948).

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