Riemann Hypothesis
Unified Field Theory
UFT toolbox I
UFT toolbox II
UFT & HD
Euler-Mascheroni
Literature
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