= Quantum field theory
{tag=Ciro Santilli's fetishes}
= QFT
{c}
{synonym}
{title2}
Theoretical framework on which quantum field theories are based, theories based on framework include:
*
*
so basically the entire
The basic idea is that there is a field for each particle particle type.
E.g. in QED, one for the and one for the : https://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 .
One way to look at QFT is to split it into two parts:
* deriving the Lagrangians of the : . 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 is unable to understand, TODO .
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: .
There appear to be two main equivalent formulations of quantum field theory:
*
*
\Video[https://www.youtube.com/watch?v=MmG2ah5Df4g]
{title=Quantum Field Theory visualized by English (2020)}
{description=
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.
* https://youtu.be/MmG2ah5Df4g?t=209 describes how the is directly related to how much you have to rotate an element to reach the original position
* https://youtu.be/MmG2ah5Df4g?t=480 explains which particles are modelled by which spin number
}
\Video[https://youtu.be/zNVQfWC_evg]
{title=Quantum Fields: The Real Building Blocks of the Universe by (2017)}
{description=
Boring, does not give anything except the usual blabla everyone knows from Googling:
* https://youtu.be/zNVQfWC_evg?t=1335 shows https://www.youtube.com/watch?v=9TJe1Pr5c9Q from
* https://youtu.be/zNVQfWC_evg?t=1522 alludes to the
}
\Video[https://www.youtube.com/watch?v=QPAxzr6ihu8]
{title=Quantum Field Theory: What is a particle? by (2021)}
{description=Gives some high level analogies between high level principles of and in to suggest that there is a minimum quanta of a relativistic quantum field.}
= Quantum field
{parent=Quantum field theory}
= Mathematical formulation of quantum field theory
{parent=Quantum field theory}
TODO holy crap, even this is hard to understand/find a clear definition of.
The , OK, is a , so we can easily understand its definition with basic calculus. We may not be able to solve it efficiently, but at least we understand it.
But what the heck is the mathematical model for a quantum field theory? TODO someone was saying it is equivalent to an infinite set of PDEs somehow. Investigate. Related:
* https://www.reddit.com/r/AskPhysics/comments/74qeag/what_is_so_hard_about_qft_after_all/
* https://physics.stackexchange.com/questions/337423/what-are-quantum-fields-mathematically
* https://physics.stackexchange.com/questions/155608/what-is-a-quantum-field
The might actually be the most understandable formulation, as shown at .
The formulation of QFT also appears to be a form of infinite-dimentional calculus.
chapter 1. "The uncertainty principle in the relativistic case" contains an interesting idea:
\Q[
The foregoing discussion suggests that the theory will not consider the time dependence of particle interaction processes. It will show that in these processes there are no characteristics precisely definable (even within the usual limitations of quantum mechanics); the description of such a process as occurring in the course of time is therefore just as unreal as the classical paths are in non-relativistic quantum mechanics. The only observable quantities are the properties (momenta,
polarizations) of free particles: the initial particles which come into interaction, and the final particles which result from the process.
]
= Gauge theory
{parent=Mathematical formulation of quantum field theory}
{wiki}
The term and idea was first introduced initialized by when he was working on combining and to formulate in 1918 and published as . Based on perception that __ symmetry implies . The same idea was later adapted for , a context in which is has even more impact.
= Lattice gauge theory
{parent=Gauge theory}
{wiki}
= Gauge field
{parent=Gauge theory}
A random field you add to make something transform locally the way you want. See e.g.: __