Riemann Hypothesis
Unified Field Theory
UFT toolbox I
UFT toolbox II
Who I am

The toolbox of the proposed unified plasma, quantum und gravity field theory covers among other things the mathematical areas

- orthogonal decompositions of Hilbert spaces
- potential operators defined by indefinite inner products
- Krein spaces in a quarternionic setting
- variational (approximation) methods in Hilbert scales
- the complex Lorentz group and its two connected components
- classical & quantum tensor theory
- quantum (two-component) spinor theory
- two-component Magnetohydrodynamics.

 The Hilbert scale decompositions model appropriately defined (quantum element and quantum energy) Hilbert spaces. More specifically, there is an energy Hilbert space H(1/2), which is decomposed into a kinematical sub-Hilbert space H(1) and an orthogonal closed "ground state energy" space H(1,ortho). The kinematical Hilbert space H(1) is governed by a countable orthogonal Riesz basis enabled by the eigen-pairs of a (kinematical) selfadjoint, positive definite operator with domain H(1). Geometrically speaking, the kinematical Hilbert space H(1) can be interpreted as a coarse-grained embedded Hilbert sub-spaces of H(1/2). The related closed (ground state energy) sub-space H(1,ortho) is governed by a continuous spectrum.

We note that the above proposed new „conceptual elements“ match to the "unconventional features of the mathematical formalism" in (HeW).


Braun K., The boundary layer A-B, the 3D-unit-sphere and space-time

Braun K., A distributional Hilbert space framework to prove the Landau damping phenomenon
                                                August 2018                                                


Braun K., An integrated electro-magnetic plasma field model

                                              September 2018


Braun K., An alternative Schroedinger (Calderon) momentum operator enabling a quantum gravity model

                                              Dec 31, 2017


Braun K., Comparison table, math. modelling frameworks for SMEP and GUT

                                              May 29, 2017


Braun K., Some remarkable Pseudo-Differential Operators of order -1, 0, 1

                                                 January 2015


Braun K.,The Prandtl (hyper singular integral) operator with double layer potential

                                                  April 2016

Braun K. Generalized wavelet theory and non-linear, non-periodic boundary value Problems

                                                  May 2016


Braun K., Unusual Hilbert or Hoelder space frames for the elementary particles transport (Vlasov) equation

                                                Februar 2018


Braun K. , A new ground state energy model

                                            August 18, 2013

further supporting data

Alpay D., et. al., Inner Product Spaces and Krein Spaces in the Quaternionic Setting

(AlO) with an alternative approach to explain the fine structure constant, question mark

Alfven H., Double layers and circuits in astrophysics


Anderson J., Ludwig Prandtl s Boundary Layer


Arbab A. I., The generalized Newton s law of gravitation

Arab A. I., The Generalized Newton s Law of Gravitation versus the General Theory of Relativity


Arab A. I., A quarternionic unification of electromagnetism and hydrodynamics

I. Aref eva Quantization of the Riemann Zeta-Function and Cosmology.pdf


Aref eva I. Y., Volovich I. V., On the Null Energy Condition and Cosmology


Arntzenius F., The CPT Theorem, ex Philosophy of Time

Azizov T. Y., et all, On Krein s papers in the theory of spaces with an indefinite metric


Barbour J., Scale invariant gravity, particle dynamics


Barbour J. B., Time and complex numbers in canonical quantum gravity


Bartholomew A., Hidden Nature, The Startling Insights of Viktor Schauberger

Bauer W. D., The Maxwell equations including magnetic monopoles

(BoD) Bohm D., Wholeness and the Implicate Order, Routledge Classics, New York, 1980

Bourgain J., Kozma G., One cannot hear the winding number


Cap F. Lehrbuch der Plasmaphysik und MHD, Paragraph 1


Calin O. et. all, SubRiemannian Geometry on the Sphere(3)

(CoJ) Coates J., Sujatha R., Cyclotomic Fields and Zeta Values, Springer, Berlin, Heidelberg, New York, 2006

(CoJ) Coates J., Sujatha R., Cyclotomic fields and zeta values

(ChD) Christodoulou D., Klainerman S., The Global Nonlinear Stability of the Minkowski Space, Princeton University Press, Princeton, 1993


Costabel M., Coercive Bilinear Form for Maxwell s Equations


Dahlke S., Weinreich I., Wavelet Bases Adapted to Pseudodifferential Operators


Dee K., Thermodynamics, gravity and universe creation


Dehnen H. et. al., Ein heuristischer Zugang zur allgemeinen Relativitätstheorie


Duffin R. J., Yukawan potential theory


Duffin R. J., Hilbert Transforms in Yukawan Potential Theory


EHRENHAFT F., 10 Vorlesungen zur Photophorese, SS 1947, Wien


Ehrenhaft F., Banet L, Magnetization of Matter by Light, Nature, 1941


Ehrenhaft F., Photophorese and its interpretation by electric and magnetic ions


Ehrenhaft F., The Magnetic Current, Nature, 1944

Ehrenhaft F., The decomposition of Water by so-called Permanent Magnet and ....


Einstein A., Ritz W., On the present status of the radiation problem, (1909)


Einstein A., Ether and the theory of relativity


Einstein A., The meaning of relativity

Einstein A., Podolsky B., Rosen N., Can Quantum-Mechanical Description of Physical Reality Be Considered Complete

Farge M., Schneider K., Wavelet transforms and their applications to MHD and plasma turbulence, a review


Geshwind Pseudodifferential Operators on SU(2).pdf


Glowinski R. et al., wavelet methods in computational fluid dynamics

Goedel K., An Example of a New Type of Cosmological Solutions of Einstein´s Field Equations of Gravitation


Hamel G., Spiralfoermige Bewegungen zaeher Fluessigkeiten


Harthun N., Wasserstrahlung mit merkwürdigen Nebenwirkungen

Heisenberg W., Introduction to the Unified Field Theory of Elementary Particles


Hopf E., Ergodentheorie


Horvath H., Photophoresis, a Forgotten Force, question marks


Howald-Haller M., Ueber die Bewegung kleiner Teilchen im Licht (Photophorese)

Ivanov S. A., Nonharmonic Fourier Series in the Sobolev Spaces of Positive Fractional Orders


Kim, H., Origin of the Universe, A Hint from Eddington-inspired Born-Infeld gravity


Kirchhoff G., Ueber die Bewegung eines Rotationskörpers in einer Fluessigkeit


Kolb E., Wolfram S., Spontaneous symmetry breaking and the expansion rate of the early universe


Kowalenko V., Frankel N. E., Asymptotics for the Kummer function of Bose plasma


Krausshar R.S., A Characterization of conformal mappings in R(n4) by a formal differentiability condition


Kummer s work on cyclotomic fields


Kummer s main theorem


Lebedev N. N., Special Functions and their Applications

Linde A., Inflation, Quantum Cosmology and the Anthropic Principle


LeFloch P. G., Ma Y., The global nonlinear stability of Minkowski space

Longitudinal plasma oscillations and Landau damping


Mijajlovic Z., Regulary Varying solutions of Friedman equation


Miyamoto K., Fundamentals of Plasma Physics and Controlled Fusion

Nag S., Sullivan D., Teichmüller theory and the universal period mapping via quantum calculus and the H(1 2) space on the circle

Naselesky P. D., Novikov D. I., Noyikov I. D., The Physics of the Cosmic Microwave Background


Nimtz G., On superluminal tunneling


Nitsche J. A., The regularity of piecewise defined functions with respect to scales of Sobolev spaces

Nitsche J. A., overview lecture notes, Hilbert scales, Approximation Theory, Non Linear Problems


Nitsche J. A., lecture notes, approximation theory in Hilbert scales

Nitsche J. A., lecture notes, approximation theory in Hilbert scales, extensions and generalizations


Nitsche J. A., lecture notes, nonlinear problems


J.A. Nitsche FEM for Conformal Mappings.pdf


Quinn J. A., A complex quaternion model for hyperbolic 3-spaces


Salih M., Quaternionic quantum wave equation and applications

Santos G. M., A debate on magnetic current, the troubled Einstein-Ehrenhaft correspondence


Viktor Schauberger s and Edward Leedskalnin s view of the world


Schauberger V. u. W., Sonderheft Mensch und Technik, 1982


Schauberger V., Die Forellenturbine


Schroedinger E.,What-is-Life


Schroedinger E., Mind and Matter


Schroedinger E., My view of the world, seek for the road

Schrödinger E., Die Erfuellbarkeit der Relativitaetsforderung in der klassischen Mechanik


Sciama D. W., On the origin of inertia

Sergeev A. G., Quantization of the Sobolev Space of Half-Differentiable Functions, II

(StR) (1-3) The Lorentz and Poincare groups

(UnA) Unzicker A., The mathematicalreality, Why Space and Time are an Illusion

(UnA1) Unzicker A., Einstein's Lost Key - How We Overlooked the Best Idea of the 20th Century

(UnA2) Unzicker A., Bankrupting Physics, How Today's Top Scientists are Gambling Away Their Credibility

(VeW) Velte W., Direkte Methoden der Variationsrechnung, B. G. Teubner, Stuttgart, 1976


Villani C., lecture notes on Landau damping


Voight J., Quaternion Algebras


Wavelets, a mathematical microscope tool

(WeH) Weyl H., Philosophy of Mathematics and Natural Science, Princeton University Press, Princeton and Oxford, 2009

(WeH1) Weyl H., Space, Time, Matter, Dover Publications., Inc., 1922

Werner P., Self-Adjoint Extensions of the Lapalce Operator with Respect to Electric and Magnetic Boundary Conditions

Werner P., Spectral Properties of the Laplace Operator with respect to Electric and Magnetic Boundary Conditions


Yan-Bin Jia, Quaternions and Rotations