Mainstream theoretical physics applies the stationary action principle to derive Lagrangian equations. This cannot explain the origin of electrical charges and cannot explain the shortlist of elementary particle types described in the Standard Model of the experimental particle physicists. See Preprint The setbacks of theoretical physics
The paper introduces geometrical symmetries and phase transitions in number systems, private parameter spaces, and symmetries in Hilbert spaces and systems of Hilbert spaces that apply the same underlying vector space. It is a textbook on advanced aspects of Hilbert spaces and treats quaternionic functions and differential calculus in detail.
The symmetries are the starting point. So it's U(1) gauge invariance and global Lorentz invariance (along with the assumption that the equations of motion don't contain more than two time derivatives) that describe all the properties of electric charges.
These are the assumptions, from which the electromagnetic properties of matter and radiation are derived.
It's possible to write down a consistent quantum field theory for any compact gauge group. It's the result of experiment that the electromagnetic properties of matter are described by a Lorentz invariant gauge theory, when the gauge group is U(1).
Similarly it's the result of experiment that the properties of particles, that are subject to the strong interactions are described by Lorentz invariant gauge theory, when the gauge group is SU(3) and, similarly, for the weak interactions, the gauge group turns out to be SU(2)Lx U(1)Y. And it's the result of experiment that these are the observable interactions, when gravitational effects can be taken to be classical.
The consistency of the description of the weak interactions then implies that the sum of the electric charges of the leptons must equal the sum of that of the quarks.
But the values of the masses of the particles, that make up matter, aren't constrained by any symmetry principle. There doesn't seem to be any particular reason why the mass of the electron-the lightest charged lepton-must be about 2000 times smaller than that of the proton-the lightest charged baryon, for instance. The consistency of the theory doesn't depend on that ratio being close to 2000.
@Stam Nicolis
Symmetry groups fail to explain the origin of electric charges because the charges relate to differences in geometric symmetry. Quaternionic differential calculus already describes the dynan]mics of fields and does that without the gauges that complex functions leave unsettled. Please study the difference between quaternionic differential calculus and vector analysis. The generations of fermions use the same electric charges as the first generation. Only their masses differ. It is suggested that leptons oscillate between their generations and that generations are oscillation modes. Only isotropic leptons can deform the field that embeds them. Quarks are not isotropic but baryons are. Baryons are conglomerates of quarks.
Physics study is and has been stopped because the basic foundation (read postulates, assumptions) needs to be re-thought. So, what can be the assumptions that can result in explanation of the big and the small observations.
For example, "electric charges" are mentioned. What is the base of this? What is the problems wherein ad hoc assumptions needed to added? My own solution is to see the nucleus of atoms as problematic for the particles-have-charge concept.
The Strong and Weak forces (forces are not like a body - ponderable) are necessary only because they are needed because we assume protons have charge. I suppose / postulate charge is illusory and the particle have magnetic characteristics. Then these force are unnecessary.
Because it equates symmetry and invariance.
Nature generates immutability out of asymmetry.
This is the same as the generation of time crystals from a non-equilibrium state.
Preprint Time-light relativity theory
Preprint Exact solution of the perihelion motion of Mercury from Newt...
>>>Why owns theoretical physics still no reliable and consistent foundation?
Because to err is human, but to admit mistakes is not.
Chords (quantum spectrum *, strings) express spacetime, life (spirit), etc., are universal laws of nature.
Preprint Chord Language
Xiaohong Li
You are wrong. These theories are not well-founded. Read Preprint The setbacks of theoretical physics
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