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, (BrK0) pp. 10-13. 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 conceptual design of the fundamental dynamical Hamiltonian operator is enabled by the Krein space theory, which is basically the theory of linear spaces with an indefinite metric. 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, (BrK0) pp. 1, 27-29, 36. The commutator of two each of those quanta system specific self-adjoint dynamic potential operators are accompanied by a well known result in form of a "variance inequality" enabling an uncertainty principle, (DaS) Theorem 2.1, (FoG), (NeJ).

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 "Perfect 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 integrated Krein space based dynamic quanta systems can be approximated by an energetical H(1/2) Hilbert space framework accompanied by the concepts of a dynamic fluid particle and a related dynamic potential operator, (BrK0) pp. 10, 11, 17-19, 38. The dynamic potential operator can be interpreted as a compact disturbance of the linear mechanical Laplacian potential operator. This approximation modelling framework is in line with Plemelj’s extension of a mass density concept (accompanied with the concept of a single layer potential) to a mass element concept (accompanied with the concept of a double layer potential), (PlJ). It enables a reduction of the Neumann problem to a hypersingular integral equation with double layer potential accompanied by a well defined (i.e. equipped with an appropriate Hilbert space domain) Prandtl operator, (LiI).

The energetical mechanical-dynamic approximation Hilbert space H(1/2) of the integrated Krein space based dynamic quanta systems enables a solution of the 3D-NSE problem. It also provides a modified Schrödinger 2.0 momentum operator (enabled by the Riesz operator), which is in line with the intrinsic self-adjoint dynamic potential operator of a Krein space based framework.

Note: 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.

Note: The dynamic quanta are characterized by quanta numbers less or equal than one; the mechanical quanta are characterized by quanta numbers greater than one.

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.


Scope

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. 


Conceptual design elements

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.

Note: 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.

Note: 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. The Lorentz transformation in special relativity is a simple type of rotation in hyperbolic space. In (LeS) new real linear quaternions are introduced to obtain a quaternionic version of the Lorentz group (without the use of complexified quaternions) and a quaternionic metric tensor is defined, overcoming difficulties concerning the appropriate transformations on the space-time.

Note: 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).

Note: The spin of an elementary particle is its eigen-rotation with exactly two rotation axes, one parallel and one anti-parallel axis to a magnetic field. This is the  complex number scheme, where every „normal“ rotation is contained twice. Consequently, an electron has a charge only half of the Planck’s quantum of action. For a quaternionic equation representation of the motion of a particle with an electric charge in a electromagnetic field manifesting the relativistic covariance of classical electromagnetism we refer to (GiP). In (ArA) a quaternionic unification of electromagnetism and hydrodynamics is provided. In (SaM) a generalized quaternionic quantum wave equation formulation is used to construct general plane waves enabling corresponding generalized Klein Gordon and Helmholtz equations.

Note: 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.

Note: 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). 

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 quanta systems can be aggregated/approximated by the purely Hilbert (energy) space system H(1/2). It is an extension of the variational mechanical standard energy Hilbert space H(1). The energy Hilbert space H(1) is the domain of the Friedrichs extension of the classical Laplacian (potential) operator accompanied by the domain H(2). Its related single layer singular integral operator accompanied by the distributional Dirac function provides the mathematical framework for the Newton/Coulomb potential.

The standard Hilbert space systems H(1) resp. H(2) also 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.

PPM & 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. The a priori PPM enables an integrated Plasma Dynamic Theory (PDT).

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