The proposed Unified Field Theory (UFT) provides an all-encompassing theory, where physical models of different physical areas are no longer decoupled and differently scaled according to their different levels of granularity. It is governed by two types of energy, the today’s mechanical energy (i.e., kinetic and potential energy) and a newly proposed dynamic energy, (which is in line with Planck's dynamic type of physical law, (PlM)), and a corresponding hierarchy of dynamic quanta accompanied by an appropriately defined scheme of quanta numbers. 

The essential mathematical concept is a Krein space framework. The crucial differentiator between Krein and Hilbert spaces is the concept of an indefinite metric/norm. The counterpart of the definite norm induced by the inner product of a Hilbert space in a Krein space framework is given by the concept of an intrinsic self-adjoint "potential" operator (the fundamental J-inner product, e.g. (BoJ) p. 120 ff). It enables the definition of quantum type specific "dynamic energy" inner products for each considered quanta energy system. 

Note: An indefinite metric in a Hilbert space is one of the unconventional features of Heisenberg's "Introduction to the Unified Field Theory of Elementary Particles", (HeW). The conceptual design of the proposed quanta scheme follows the "principle of Nature" that any "action" always requires a potential difference or a "pressure", i.e., there is no physical action, just because there is energy or a potential. Technically speaking, all Krein space based particle types are elements of the same underlying baseline Hilbert space; however, they are accompanied by different (energetical) indefinite & definite inner products and norms (functionals) for each considered quanta.



Scope & conceptual design elements

The scope of the Unified Field Theory (UFT) includes the scope of the three (independent, just "linked because they seem to have similar characteristics", (GlJ) p. 433) quantum field theories (strong interactions, weak interactions, and electromagnetics), the scope of both relativity theories, the plasma physics, and the solid state physics. 

The Hilbert space theory provides the mathematical framework of quantum mechanics. The extended Krein space theory (accompanied by the concepts of an indefinite norm and an intrinsic self adjoint potential operator) provides the mathematical framework of the proposed UFT. While quantum mechanics is governed by the physical concept of mechanical energy, the proposed quanta dynamics is governed by mechanical and (newly) dynamic energy. There are several dynamic quanta systems, which are governed by an appropriately defined deductive quanta numbers scheme. The characteristic of this scheme is an implicate (in the sense of D. Bohm, (BoD1)) "potential difference" between the related (particle,anti-particle)-components per each quanta system.

The real Lorentz group L has three subgroups (orthochronous, proper, orthochorous). Associated with the restricted Lorentz group is the group of 2x2 complex matrices of determinant one, which is denoted by SL(2,C). It is isomophic to the symmetry group SU(2) and the unit quaternions S(3). In SMEP the group SU(2) describes the weak force interaction with 3 bosons W(+), W(-), Z, the characteristic of the beta-decay process. It also plays a key role in the special relativity theory accompanied by the concept of the Minkowski space.

The perhaps primary application of quaternions is the quaternion rotation operator addressing the „translation-rotation“ (linear and angular rotation) „permutation“ requirement. This is a special quaternion triple-product (unit quaternions and rotating imaginary vector) competing with the conventional (Euler) matrix rotation operator, (BrK0) p. 47, (KuJ).

The  complex Lorentz group L(C) is associated with SU(2)xSU(2). It is essential in the proof of the PCT theorem, (StR) p. 13. It is also the (hidden) symmetry group of the Coulomb problem, (BrK0) p. 58 ff., (BrK14) pp. 14, 28. In contrast to the real Lorentz group the complex Lorentz group has just two connected (!) components accompanied by a multiplication law for pairs of 2x2 matrices, (StR) p. 14. It is supposed to govern the conservation of energy laws of the dynamic quanta systems, (BrK0) p. 31.

There are two a priori 2-component mathematical dynamic quanta systems: the a priori dynamic electrino-positrino based ground state quanta system and the electron-positron based perfect plasma quanta system, see also (BrK14) p. 26. The most aggregated Krein space based energetical systems built from those a priori systems are three types of explicate 1-component mechanical atomic nucleus quanta systems accompanied by implicate 1-component dynamic quanta systems (ref. Bohm's "wholeness and implicate & explicate orders", (BoD1)). They may be interpreted as conductor, semi-conductor, and non-conductor atomic nucleus types.

The UFT provides a

- 2-component a priori dynamic "Ground State" Model (GSM)
- 2-component a priori dynamic "Perfect Plasma" Model (PPM)
- 2-component mechanical "Electro-Magnetic" Maxwell-Mie Theory (EMT)
- 1-component mechanical "Dirac 2.0 Atomic Nucleus" Theory (ANT)
- 1-component Dynamic Fluid Theory (DFT).

It enables

- a well-posed 3D-NSE system for dynamic fluid particles by the DFT
- an enhanced Schrödinger 2.0 operator by the Riesz transform
- a "Yang-Mills" SU(2)-invariance for Dirac 2.0 (mass) particles by the ANT
- an integrated Plasma Dynamics Theory (PDT).

The symmetry break down from the complex Lorentz group to the (real) restricted Lorentz group may become a characteristic of the transformation process from purely dynamic energy governed 2-component quanta systems to 1-component quanta systems accompanied by the concept of mechanical energy and the Minkowski space-time continuum.


GSM & PPM
The a priori 2-component dynamic "Ground State" Model (GSM) and the a priori dynamic "Perfect Plasma" Model (PPM) may be interpreted as an Einstein-Lorentz ether, (EiA5). We note that

- the CMBR (currently interpreted as the "echo of the early universe", (LaM)) is an essential element of theoretical and observational cosmology and one of the foundation stones of the big bang models; to the author's humble opinion, those models are extremely unrealistic because they are based on an a priori required mathematical singularity which caused for whatever reason the biggest explosion ever, (PeR) p. 444

- there are currently two different (!) physical explanation models for the Landau damping phenomenon depending from the considered linear or nonlinear mathematical model, (BrK14) p. 18.

The cosmic microwave background radiation (CMBR) and the Landau damping phenomena may be interpreted as characteristic (echo) phenomena of the EMT electroton-magneton quanta creation process from the GSM and PPM, see also (BrK14) p. 26.

EMT
Quote: „…. light beams must have electric stationary components in the direction of the wave front normal, and that consequently there must be stationary electric potential differences between different points along the beam; and that there must be also a stationary magnetic field in the beam of light with potential differences. Hence, the light beam must have a magnetizing effect, and the charge of a magnet should be changed by light“, (EhF1).

We note that the mechanical energy based 2-component electro-magnetic quanta field of the EMT is in line with the "photopheresis" phenomenon discovered by F. Ehrenhaft, (BrJ), (BrK14) p. 22.

ANT
In the ANT the term "Dirac 2.0 Atomic Nucleus" is chosen to anticipate that Dirac's single mechanical energy system is extended to a mechanical x dynamic energy system concept. 

Quote: "Dirac's theory of radiation is based on a very simple idea; he treats an atom and the radiation field as a single system whose energy is the sum of three terms: one representing the energy of the atom, a second representing the electromagnetic energy of the radiation field, and a small term representing the coupling energy of the atom and the radiation field", (FeE).

The Dirac 2.0 systems provide a mechanical atomic nucleus concept accompanied by the concept of implicate dynamic quanta (in the sense of D. Bohm, (BoD1)). The potential between this implicate quanta pair defines the dynamic energy of the mechanical atomic nucleus. Those systems neither require the hypothesis of an electron spin nor the existence of the fine structure constant.

The ANT puts the spot on the "Mach 2.0" principle as proposed in (UnA1) p. 156, which is essentially the Mach principle + Dirac's two large number hypotheses in the context of his "new basis for cosmology", (DiP2).

DFT
The Krein space based 1-component mechanical atomic nucleus quanta systems can be further aggregated/approximated by the purely Hilbert (energy) space system H(1/2), which is an extension of the variational mechanical standard energy Hilbert space H(1). The mechanical H(1) energy system is the domain of the Friedrichs extension of the Laplacian (potential) operator accompanied by the domain H(2), i.e. it is an extension of the classical mechanical standard energy Hilbert space H(2).

The standard Hilbert space systems H(1) resp. H(2) provides the variational resp. the classical framework for classical and quantum mechanics accompanied by the concept of Fourier waves. The complementary sub-space of the extended H(1/2) Hilbert space with respect to the H(1)-norm provides an appropriate Hilbert space based framework for quantum dynamics accompanied by the concept of wavelets. The latter ones may be interpreted as "a mathematical microscope", (BrK0) p. 19, (BrK14) p. 37, (HoM) 1.2.

Physically speaking, the compact embedding of H(1) into H(1/2) addresses "the problem of matter in the Maxwell equations, by explaining why the field possesses a granular structure and why the knots of energy remain intact in spite of the back-and-forth flux of (mechanical!) energy and momentum", (WeH) p. 171.

PDT
Plasma is that state of matter in which the atoms or molecules are found in an ionized state. The number of neutral particles (atomes or molecules) in a gas is irrelevant for the definition of a plasma. The number of positively and negatively charged particles per considered volume element may be arbitrarily small oder arbitrarily large, but both numbers need to be approximately identical (in order to have no internal macroscopic electrostatic  fields. The interactions of electrons and ions are determined by long-range electrical forces. Plasma physics is about classical statistical fluid mechanics and classical fluid dynamics. The underlying related mathematical models are grouped by different physical application areas resp. chosen mathematical tools accompanied by correspondingly defined different types of „plasma matter gases“, (BrK0) p. 60.

Note: The a priori GSM & PPM in combination with the EMT, ANT and DFT enable an integrated Plasma Dynamics Theory (PDT) avoiding the concept of a Debye sphere.

Braun K., The deductive structure of the UFT, creative vacuum and perfect plasma, and related opportunities.pdf

 
                                                  June, 2025

Braun, K., An unified field theory enabling a deductive structure of physics.pdf

 

                                               December 2022




                                  

Braun K., UFT related list of papers

 

                                        Earlier UFT related papers