This one might actually be understandable! It is what Richard Feynman starts to explain at: Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979).
The difficulty is then proving that the total probability remains at 1, and maybe causality is hard too.
The path integral formulation can be seen as a generalization of the double-slit experiment to infinitely many slits.
Feynman first stared working it out for non-relativistic quantum mechanics, with the relativistic goal in mind, and only later on he attained the relativistic goal.
TODO why intuitively did he take that approach? Likely is makes it easier to add special relativity.
This approach more directly suggests the idea that quantum particles take all possible paths.
Theoretical framework on which quantum field theories are based, theories based on framework include:so basically the entire Standard Model
The basic idea is that there is a field for each particle particle type.
E.g. in QED, one for the electron and one for the photon: physics.stackexchange.com/questions/166709/are-electron-fields-and-photon-fields-part-of-the-same-field-in-qed.
And then those fields interact with some Lagrangian.
One way to look at QFT is to split it into two parts:Then interwined with those two is the part "OK, how to solve the equations, if they are solvable at all", which is an open problem: Yang-Mills existence and mass gap.
- deriving the Lagrangians of the Standard Model: why do symmetries such as SU(3), SU(2) and U(1) matter in particle physics?s. This is the easier part, since the lagrangians themselves can be understood with not very advanced mathematics, and derived beautifully from symmetry constraints
- the qantization of fields. This is the hard part Ciro Santilli is unable to understand, TODO mathematical formulation of quantum field theory.
There appear to be two main equivalent formulations of quantum field theory:
Quantum Field Theory visualized by ScienceClic English (2020)
Source. Gives one piece of possibly OK intuition: quantum theories kind of model all possible evolutions of the system at the same time, but with different probabilities. QFT is no different in that aspect.- youtu.be/MmG2ah5Df4g?t=209 describes how the spin number of a field is directly related to how much you have to rotate an element to reach the original position
- youtu.be/MmG2ah5Df4g?t=480 explains which particles are modelled by which spin number
Quantum Fields: The Real Building Blocks of the Universe by David Tong (2017)
Source. Boring, does not give anything except the usual blabla everyone knows from Googling:Quantum Field Theory: What is a particle? by Physics Explained (2021)
Source. Gives some high level analogies between high level principles of non-relativistic quantum mechanics and special relativity in to suggest that there is a minimum quanta of a relativistic quantum field.Bibliography review:
- Quantum Field Theory lecture notes by David Tong (2007) is the course basis
- quantum field theory in a nutshell by Anthony Zee (2010) is a good quick and dirty book to start
Course outline given:
- classical field theory
- quantum scalar field. Covers bosons, and is simpler to get intuition about.
- quantum Dirac field. Covers fermions
- interacting fields
- perturbation theory
- renormalization
Non-relativistic QFT is a limit of relativistic QFT, and can be used to describe for example condensed matter physics systems at very low temperature. But it is still very hard to make accurate measurements even in those experiments.
Defines "relativistic" as: "the Lagrangian is symmetric under the Poincaré group".
Mentions that "QFT is hard" because (a finite list follows???):But I guess that if you fully understand what that means precisely, QTF won't be too hard for you!
There are no nontrivial finite-dimensional unitary representations of the Poincaré group.
Notably, this is stark contrast with rotation symmetry groups (SO(3)) which appears in space rotations present in non-relativistic quantum mechanics.
www.youtube.com/watch?v=T58H6ofIOpE&t=5097 describes the relativistic particle in a box thought experiment with shrinking walls
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.
Sponsored by National Academy of Sciences, located in Long Island.
Some photos at: www.nasonline.org/about-nas/history/archives/milestones-in-NAS-history/shelter-island-conference-photos.html on the website of National Academy of Sciences, therefore canon.
This is where Isidor Rabi exposed experiments carried out on the anomalous magnetic dipole moment and Willis Lamb presented his work on the Lamb shift.
It was a very private and intimate conference, that gathered the best physicists of the area, one is reminded of the style of the Solvay Conference.
QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) chapter 4.1 this conference was soon compared to the First Solvay Conference (1911), which set in motion the development of non-relativistic quantum mechanics.