A quanta field theory
Riemann Hypothesis
Goldbach & Kummer
Who I am


                                              E. Schrödinger

                                     The principle of objectivation

"Science aims at nothing but making true and adequate statements about its object. The scientist only imposes two things, namely truth and sincerity, imposes them upon himself and upon other scientists. In the present case the object is science itself, as it has developed and has become and at present is, not as it ought to be or ought to develop in future", (ScE1) p. 117


                                               E. Schrödinger

                        Form, not substance, the fundamental concept

„The new idea is that what is permanent in these ultimate particles or small aggregates is their shape and organization. The habit of everyday language deceives us and seems to require, whenever we hear the word „shape“ or „form“ pronounced, that it must be the shape or form of something, that a material substratum is required to take on a shape. Scientifically this habit goes back to Aristotle, his causa materialis and causa formalis. But when you come to the ultimate particles constituting matter, there seems to be no point in thinking of them again consisting of some material. They are, as it were, pure shape, nothing but shape; what turns up again and again in successive observations is this shape, not an individual speck of material“, (ScE3) p. 12


                                                 B. Russell

           Space and time as forms of "intuition" ("Anschauung") by Kant

Hume had proved that the law of causality is not analytic, and had inferred that we could not be certain of its truth. Kant accepted the view that it is synthetic, but nevertheless maintained that it is known a priori. He maintained that arithmetic and geometry are synthetic, but are likewise a priori. He was thus led to formulate his problem in these terms:

How are synthetic judgements a priori possible?

The answer to this question, with its consequences, constitutes the main theme of The Critique of Pure Reason.

Space and time, Kant says, are not concepts; they are forms of „intuition“. (The German word is „Anschauung“, which means literally „looking at“ or „view“. The word „intuition“, though the accepted translation, is not altogether a satisfactory one.) (RuB1) p. 680

                               The proposed quanta field theory

The proposed quanta field theory is based on coherently defined physical quanta, which are different types of energetical (mechanical or dynamical) quantum elements. They are appropriately composed by two abstract (mathematical) quanta forming a "ground state energy" quanta field in line with the thoughts in (DaJ).

The proposed quanta field theory 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. In particular, the integrated physical three layer modelling framework

- enables a solution of the 3D-Navier-Stokes Millennium Problem of the Clay Mathematics Institute

- overcomes the physical "YME mass gap" Millennium Problem of the Clay Mathematics Institute by making those equations obsolete

- provides an appropriate mathematical model for the Landau damping phenomenon

- is accompanied by a H(1/2) based overall energy Hilbert space in line with the Teichmüller theory & the universal period mapping via quantum calculus, (NaS), and the appropriate domains of the double layer (Prandtl) potential operator as applied e.g. in aerodynamics, (LiI)

- supports the aspiration of A. Unzicker's "mathematical reality", to "form a consistent picture of reality by observing nature from the cosmos to elementary particles," (UnA2).

The essential ingredient of the proposed quanta field theory: a second dynamical energy type avoiding the concepts of fermions and bosons

Classical mechanics is concerned with kinematics and dynamics. The kinematics deals with the different forms of the movement of bodies in a space-time environment. Classical dynamics should explain the reasons of the connection of those different form of movements. The principle of transfer causality („Impetustheorie“, "impetus ~ momentum" (WoM)) states that a transfer of movements requires the mediation of a certain type of quantum, a "transfer force quantum".

In simple words, the proposed new structure of theoretical physics (coming along with a mathematical explanation of quantum numbers) overcomes the three decoupled fermions (kinematics) & bosons (dynamics) quantum types (= quanta) worlds of the related three decoupled theories building the so-called Standard Model of Elementary Particles (requiring multiple arbitrary parameters). It comes along with new types of matter including plasma matter. Thereby, current classical (purely mechanical energy type based) kinetical and dynamical laws become classical Partial Differential Equation based mathematical approximation models (including the physical concepts of linear or angular momenta and Huygens' principle).

The proposed structure of physics accompanied by a no longer purely mechanical energy type concept is strongly related to Weizäcker's philosophy of physics, (WeC). It also suggests to revisit forgotten thoughts, discoveries and theories, e.g., Platon's theoretical philosophy (especially the relations of idea & cosmos resp. time & astronomy, (BöG),(BöG1)), Leibniz' vis viva concept, Goethe’s „data for a theory of color“ („Zur Farbenlehre“), e.g. (MüO), (NuI), (RiN), Schopenhauer’s „on vision and colours“, e.g. (HüA), (ScD) p. 33 ff., Schopenhauer’s concept of "matter as mere visibility of the will", (ScD) p. 42, Ehrenhaft’s discovery of the photophoresis phenomenon, e.g. (BrJ), Schauberger’s implosion theory for planetary movements, e.g. (BaA), and the implosion theory as the initializer of the universe creation process, (DeK).

Braun K., An integrated quanta field theory enabling a deductive structure of Physics

                                 June 10, 2024 update: pp. 85/86

Braun, K., A Krein space based quanta energy field model, supporting mathematics

The Gordian knot: current "realities" of physical and mathematical areas

Braun, K., Current physical and mathematical realities regarding an unified field Theory

The relation to the Riemann Hypothesis, the Hilbert-Polya (resp. the Berry-Keating) conjecture, Montgomery's pair correlation conjecture and the Goldbach conjecture

The Krein space based hermitian (potential) operators governing the vacuum quanta field may provide an alternative (selfadjoint) operator to the Berry-Keating "quantized" classical Hamiltonian operator of a particle of mass m that is moving under the influence of a problem specific to be defined potential function V(x).

The provided proof of the Riemann Hypothesis is based on a decomposition of the meromorphic Zeta function (occuring in the symmetrical form of the Riemann functional equation) into a sum of integral and series representations. The "symmetrical" series representations provide a characterization of the non-trivial zeros z(n)=1/2+/-it(n) of the zeta function in relation to the vertical line (1/2-2n) +/- i*t(n).

The primes (excluding the integer "2", the base number of the even numbers) are a subset of the odd integers. The conceptual design of the mathematical baseline quanta of the proposed quanta field theory, the electrinos and the positrinos forming the "ground state energy quanta field", is based on the different Schnirelmann densities of the odd resp. the even integers, a half resp. zero. Physically speaking, the Schnirelmann densities determines a kind of density distributions of the (odd integer related) electrinos and the (even integer related) positrinos of a mathematical "vacuum" quanta field. 

The  binary Goldbach conjecture states that every positive even number n>2 is the sum of two primes. The claim is, that a "prime number density decomposition" in the above sense provides an alternative method to the standard Hardy-Littlewood circle method to prove the binary Goldbach conjecture.

Braun K., A toolbox to solve the RH and to build a non-harmonic Fourier series based two-semicircle method


Polya Ueber eine neue Weise bestimmte Integrale in der Zahlentheorie zu gebrauchen

The physical Montgomery-Odlyzko law states that the distribution of the spacing between successive non-trivial zeros of the zeta function is statistically identical with the distribution of eigenvalue spacing in a "Gaussian Unitary Ensemble". The claim is that the above conceptual modelling components also enable an appropriate mathematical model, where the physical Montgomery-Odlyzko law becomes the (L(2)-space based) statistical relevant part of the zeros distribution of the zeta function on or close to the critical line. 


Braun K., The Montgomery-Odlyzko law, eigenvalue spacing in a collection of Gaussian unitary operators


(DeJ) Derbyshire J., Number theory meets quantum mechanics

UFT related historical papers:


Braun K., UFT related list of papers