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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).
 the complex Lorentz and Poincare groups |
Wavelets, a mathematical microscope tool |
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 |
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 |
Hamel G., Spiralfoermige Bewegungen zaeher Fluessigkeiten |
Heisenberg W., Introduction to the Unified Field Theory of Elementary Particles |
Ivanov S. A., Nonharmonic Fourier Series in the Sobolev Spaces of Positive Fractional Orders |
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 |
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 |
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 |
(NeJ) Neukirch, J., Klassenkörpertheorie, BI, Mannheim, Wien, Zürich, 1969
Santos G. M., A debate on magnetic current, the troubled Einstein-Ehrenhaft correspondence
Viktor Schauberger s and Edward Leedskalnin s view of the world |
Scholz E., The Concept of Manifolds, 1850-1950 |
Scholz E., Riemanns fruehe Notizen zum Mannigfaltigkeitsbegriff und zu den Grundlagen der Geometrie |
Scholz E., Hermann Weyl s Purely Infinitesimal Geometry |
Scholz E., H. Weyl s and E. Cartan s proposals for infinitesimal geometry in the early 1920s |
Scholz E., Weyl geometry in late 20th century physics |
Schroedinger E., Mind and Matter, chapter I |
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
Voight J., Quaternion Algebras |
Wavelets, a mathematical microscope tool |
(WeA) Weil A., Elliptic Functions According to Eisenstein and Kronecker, Springer, Berlin, Heidelberg, New York, 1991
(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
