Farhad Ghaboussi

University of Konstanz | Uni-Konstanz · Department of Physics

We discuss the topological aspects of mass gap problem and renormalization of quantum Yang-Mills models according to the relation between the integrability and renormalization of these models.

We describe the topological aspects of quantum phenomena and quantum vertex in accord with the experimental aspects of QED phenomena.

The topological aspects of Hodge conjecture are considered and its proof is discussed according to the differential topological structure of Hodge theory.

The topological aspects of Hodge conjecture are considered and its proof is discussed according to the differential topological structure of Hodge theory.

We consider the millennium problems of mathematics in view of unity of mathematics, topology, theory of invariants and category theory and discuss their topological aspects.

We consider the millennium problems of mathematics in view of unity of mathematics, topology, theory of invariants and category theory and discuss their topological aspects.

We conjecture a new insight on dimensional structure of physics and discuss with respect to problems of the standard model of physics the question of how many dimensions of the 3D space can be considered as independent dimensions.

We conjecture a new insight on dimensional structure of physics and discuss with respect to problems of the standard model of physics the question of how many dimensions of the 3D space can be considered as independent dimensions.

We investigate the topological structure of Navier-Stokes equations demonstrating their two dimensional topology and give arguments for why they are integrable in two dimensions (2D). Insofar in there is no solution for Navier-Stokes equations in 3D case. We prove that even the any presumed 3D solution of Navier-Stokes equations requires a distingu...

We discuss basic aspects of Riemann surface and show that it is adopted from electrodynamics on curved surfaces.

We introduce a differential topological proof and an analytical proof of Riemann hypothesis according to the saddle point method because Riemann calculated the integral representation of zeta function on the critical line by this method. This topological proof of RH proves that the existence of integral representation of zeta functions requires cer...

According to a topological analysis of emergence we define emergence as a topological property of finite physical/dynamical systems on compact manifolds and formulate the theory of emergence.

We introduce a differential topological proof of Riemann hypothesis according to the saddle point method that is applied by Riemann to calculate the integral representation of zeta function on the critical line. This topological proof of RH proves that the existence of integral representation of zeta functions requires certain differential topologi...

We introduce a differential topological proof of Riemann hypothesis according to the saddle point method that is applied by Riemann to calculate the integral representation of zeta function on the critical line. This topological proof of RH proves that the existence of integral representation of zeta functions requires certain differential topologi...

We discuss basic logical, theoretical and epistemological reasons for the long standing crisis of mathematics and theoretical physics which is manifested by the incompatibility of mathematical models of two basic theories QFT and GRT, the unsolved "foundational crisis of mathematics" and millennium problems of mathematics.

The proof of Riemann hypothesis is given according to Riemann's saddle point method which is used by him to derive the integral representation of zeta function. The topological evidence of method is also discussed.

We show that our proof of Riemann hypothesis by the saddle point method is justified by topological consideration of Riemann's integral representation of zeta function as a zero differential form represented by the integral of a differential one form according to the theory of integrability.

We discuss basic logical, theoretical and epistemological reasons for the long standing crisis of mathematics and theoretical physics which is manifested by the incompatibility of mathematical models of two basic theories QFT and GRT, the unsolved "foundational crisis of mathematics" and millennium problems of mathematics. 1 I mentioned in some of...

In view of the relations between Riemann hypothesis and quantum theory according to the Hilbert-Polya conjecture and further related investigations its proof is important also for the quantum physics. I conjecture to prove Riemann hypothesis according to Riemann's saddle point method which is used by Riemann to derive the integral representation of...

In view of the relations between Riemann hypothesis and quantum theory according to the Hilbert-Polya conjecture and further related investigations its proof is important also for the quantum physics. I conjecture to prove Riemann hypothesis according to Riemann's saddle point method which is used by Riemann to derive the integral representation of...

Riemann hypothesis is based on certain essential mathematical tools which are used by Riemann to construct the integral representation of zeta function especially on the critical line and to express the hypothesis about its non-trivial zeros. I determine these mathematical tools and show that using them one can prove the Riemann hypothesis.

In view of relations between Riemann hypothesis and quantum theory according to the Hilbert-Polya conjecture and further investigations its proof is important for quantum physics. I conjecture to prove Riemann hypothesis according to Riemann's saddle point method to derive zeta function. It is shown that the proof of Riemann hypothesis by the appli...

Further justifications for my conjecture to prove Riemann hypothesis by the physical saddle point and stationary-phase methods are discussed including the application of saddle point method to Riemann's definition of powers of primes. It is proved that σ = 1 2 is a true saddle point of zeta function according to the vanishing of its second derivati...

It is shown that the conjecture to prove Riemann hypothesis according to the saddle point method is equivalent to its proof by the application of the stationary-phase method.

We disclose the general mathematical structure of physics and show that QFT, supersymmetry and all those usual fashions are various aspects of the neglected 2D substructure of physics as the theory of integrable or structurally stable dynamical systems.

In view of relations between Riemann hypothesis and quantum theory according to the Hilbert-Polya conjecture and further investigations its proof is important for quantum physics. I conjecture to prove Riemann hypothesis according to Riemann's saddle point method to derive zeta function.

We disclose the general mathematical structure of physics and show that QFT, supersymmetry and all those usual fashions are various aspects of the neglected 2D substructure of physics as the theory of integrable or structurally stable dynamical systems.

We introduce a differential topological proof and an analytical proof of Riemann hypothesis according to the saddle point method because Riemann calculated the integral representation of zeta function on the critical line by this method. This topological proof of RH proves that the existence of integral representation of zeta functions requires cer...

We introduce the topological integration theory as a new insight on foundations of mathematics and physics according to topological invariants in the sense of solvability of mathematical and physical problems .

arXiv:2408.13292 [physics.gen-ph]. An approach to prove Riemann hypothesis is introduced according to Rie-mann's saddle point method to derive zeta function. This is a direct method to prove Riemann hypothesis related with my previous topological approach to analytic number theory and Riemann hypothesis.

An approach to prove Riemann hypothesis is introduced according to Rie-mann's saddle point method to derive zeta function. This is a direct method to prove Riemann hypothesis related with my previous topological approach to analytic number theory and Riemann hypothesis.

An approach to prove Riemann hypothesis is introduced according to Rie-mann's saddle point method to derive zeta function. This is a direct method to prove Riemann hypothesis related with my previous topological approach to analytic number theory and Riemann hypothesis.

An approach to prove Riemann hypothesis is introduced according to Rie-mann's saddle point method to derive zeta function. This is a direct method to prove Riemann hypothesis related with my previous topological approach to analytic number theory and Riemann hypothesis.

We introduce a new approach to prove Riemann hypothesis. This approach is a direct method to prove Riemann hypothesis and related with our previous topological approach to analytic number theory.

We discuss basic logical, theoretical and epistemological reasons for the long standing crisis of mathematics and theoretical physics which is manifested by the incompatibility of mathematical models of two basic theories QFT and GRT, the unsolved "foundational crisis of mathematics" and millennium problems of mathematics. 1 I mentioned in some of...

We prove that according to the theory of invariants and integrability theory the 4D classical-and quantum electrodynamics (CED) (QED) and Yang-Mills field theories are equivalent and can be reformulated as 2D Field theories which do not need renormalization because their 2D equivalent filed theories are integrable and include the renormalized resul...

We analyse the structure of topology including "differential topology" and criticize the discrepancies between the assumptions of "differential topology" and the standards of topology.

We discuss the basic aspects of illogical structure of mathematics and physics in view of "foundational crisis of mathematics" and incompatibility of QFT and GRT and design a way out of it to achieve effective and invariant results in both disciplines.

We discuss basic structure of Alexandrov spaces including their generalization of Riemann spaces, derive a new proof of the theorem about the circumference of curved geodesic triangles in these spaces and introduce a new theorem which is equivalent to that one.

We prove that 2D integrable theories are already qualitatively quantized according to the quantization as a special quantitative case of integrability. The equivalence of Bohr-Sommerfeld integral quantization and quantum commutator structure is disclosed and the relation to quantization of curved areas in quantum gravity is discussed.

We discuss methods to prove Goldbach conjecture.

We disclose the basic relation between Riemann space and Hilbert space which can be used to define quantum gravity. It is related with the topology of spaces for integrable dynamical systems 1

We show that the announced relation between number π and the string theory is an old aspect of the evaluation of 2D surface integrals in polar coordinates specially manifested in the calculation of probability of normal distribution and Γ(1 2) where π is the area of unite circle. We introduce a topological action for string theory in this respect.

We show that the announced relation between number π and the string theory is an old aspect of the evaluation of 2D surface integrals in polar coordinates specially manifested in the calculation of probability of normal distribution and Γ(1 2) where π is the area of unite circle. We introduce a topological action for string theory in this respect.

We discuss basic structure of Alexandrov spaces including their generalization of Riemann spaces, derive a new proof of the theorem about the circumference of curved geodesic triangles in these spaces and introduce a new theorem which is equivalent to that one.

We introduce geometrical and topological aspects of Hilbert space and optimal transport with respect to their common curvature concept and integrability aspect and the integral quantization of curvature. A new equation for optimal transport is also introduced and the relation between integral quantization and commutator quantization is described.

We disclose the 2D foundations and aspects of GRT and Einstein equations. These 2D basics of general relativistic gravity are useful for quantization of gravity according to the integrability and quantizability of 2D field theories.

We introduce a topological/geometrical approach to the curved geometry of optimal transport, Hilbert spaces and related topics including Sobolev spaces and Jacobi equation. A new equation for optimal transport is also introduced.

We introduce a new invariant for prime numbers according to the theory of in-variants and sketch a new approach to prove Riemann hypothesis based on this algebraic invariant. Thus our related trigonometric representation of primes is conform with Riemann's method to derive zeta function by the exponential representation of primes, as well as it is...

We clarify the geometrical background of integrable systems, lattice models and two-body interaction models in particle physics according to their topological two degrees of freedom structure (2DF). The basic concept of global 2DF (2D) geometry of equations of motion as the actual geometry or topology of integrable dynamical systems is introduced w...

The usual believe on infinite dimensionality of probability with respect to the range and the number of dimensions is traditional but incorrect. Nor the related number of orthonormal states of probability neither the range of them are infinite, both are not only finite but even two-dimensional (two degrees of freedom), i. e. always a collection of...

The usual believe on infinite dimensionality of probability with respect to the range and the number of dimensions is traditional but incorrect. Nor the related number of orthonormal states of probability neither the range of them are infinite, both are not only finite but even two-dimensional (two degrees of freedom), i. e. always a collection of...

We introduce the topological integration theory as a new insight on foundations of mathematics and physics according to topological invariants in the sense of solvability of mathematical and physical problems .

We introduce the topological integration theory as a new insight on foundations of mathematics and physics according to topological invariants in the sense of solvability of mathematical and physical problems .

We introduce the topological integration theory as a new insight on foundations of mathematics and physics according to topological invariants in the sense of solvability of mathematical and physical problems .

The usual believe on infinite dimensionality of probability with respect to the range and the number of dimensions is traditional but incorrect. Nor the related number of orthonormal states of probability neither the range of them are infinite, both are not only finite but even two-dimensional (two degrees of freedom), i. e. always a collection of...

In the last decade some authors claim that the spectral and mass gap problem of standard model of physics is undecidable 1. The mode of "undecidability" arose in mathematics, in general, for problems related with infinities, notably in the case of "continuum hypothesis". In other words, in any problem including infinity where one was not able to so...

This book is about unsolved crisis in exact sciences, physics and mathematics which arose first as the “foundational crisis of mathematics” and the crisis of physics as the incompatibility of quantum theory and general relativity theory. It is a fundamental critic of highly contradictory antiquated foundations of physics and mathematics which resul...

We investigate the efficient form to consider scientific questions and problems and describe a general algorithm to solve them in connection with decision problem.

We conjectured previously an integral operator representation of the adjoint differential operator according to the theory of pseudo-differential operators and the origination of Hodge-de Rham theory of differential topology from the differential equation of electrodynamics. Here we prove it according to the equality of analytical and topological i...

We investigate the invariant structures of integrability and analytical Euler characteristic of higher even dimensional manifolds like S 4 as the standard model of physical space-time. Their comparison and its application on a concrete example proves that invariant characters of these manifolds like finite integrals on these manifolds are decompose...

We analyse the structure of topology including "differential topology" and criticize the discrepancies between the assumptions of "differential topology" and the standards of topology.

We investigate the invariant structures of integrability and analytical Euler characteristic of higher even dimensional manifolds like S 4 as the standard model of physical space-time. Their comparison and its application on a concrete example proves that invariant characters of these manifolds like finite integrals on these manifolds are decompose...

We investigate the invariant structures of integrability and analytical Euler characteristic of higher even dimensional manifolds like S 4 as the standard model of physical space-time. Their comparison and its application on a concrete example proves that invariant characters of these manifolds like finite integrals on these manifolds are decompose...

We investigate the invariant structures of integrability and analytical Euler characteristic of higher even dimensional manifolds like S 4 as the standard model of physical space-time. Their comparison and its application on a concrete example proves that invariant characters of these manifolds like finite integrals on these manifolds are decompose...

The usual believe on infinite dimensionality of probability with respect to the range and the number of dimensions is traditional but incorrect. Nor the related number of orthonormal states of probability neither the range of them are infinite, both are not only finite but even two-dimensional, i. e. always a collection of two orthonormal states: Σ...

We introduce a new invariant for prime numbers according to the theory of in-variants and sketch a new approach to prove Riemann hypothesis based on this algebraic invariant. Thus our related trigonometric representation of primes is conform with Riemann's method to derive zeta function by the exponential representation of primes, as well as it is...

We analyse the structure of topology including "differential topology" and criticize the discrepancies between the assumptions of "differential topology" and the standards of topology.

In this note I prove that the small denominator problem is an ill posed mathematical problem which arose from the traditional local view on global problems of structural stability. The true structural stability problem is a topological 2D problem without any inclusion of small denominator problem. The artificial structure of this problem can be con...

In this note I prove that the small denominator problem is an ill posed mathematical problem which arose from the traditional local view on global problems. The true structural stability problem is a topological 2D problem without any inclusion of small denominator problem. The artificial structure of this problem can be considered in the assumptio...

In view of great interest, I concretized some of early compactified aspects) F. Ghaboussi The disaster of room temperature superconductivity in "Nature" is not the first and will be not the last one in this area just as it was the second retracted work of the same group in short time. Two decades ago, we were faced with a similar repeated forgery i...

This is a book about philosophy of mathematics and physics.

The disaster of room temperature superconductivity in "Nature" is not the first and will be not the last one in this area just as it was the second retracted work of the same group in short time. Two decades ago, we were faced with a similar repeated forgery in "nature" of Mr. Schoen in solid state physics and later with far more forgeries in this...

We investigate the structure of canonical quantization condition and prove it as integrability condition.

We analyse the structure of topology including "differential topology" and criticize the discrepancies between the assumptions of "differential topology" and the standards of topology. 1 Topology as analysis situs was invented by Leibniz in order to consider geometry from the global view avoiding local and algebraic aspects of geometry which was co...

We analyse the structure of topology including "differential topology" and criticize the discrepancies between the assumptions of "differential topology" and the standards of topology.

We introduce and discuss new topological aspects of knots and their Alexander-Jones polynomials. Topological aspects related to physics and number theory are also considered.

We conjectured previously an integral operator representation of the adjoint differential operator according to the theory of pseudo-differential operators and the origination of Hodge-de Rham theory of differential topology from the differential equation of electrodynamics. Here we prove it according to the equality of analytical and topological i...

We introduce new topological insight on instantons and index theory according to the Euler characteristic on S 2 .

According to a topological analysis of emergence we define emergence as a topological property of finite physical/dynamical systems on compact manifolds and formulate the theory of ememrgence.

We analyse the structure of differential 3-and higher forms from the stand point of topological invariance and prove that their structure is not unique and unusable in physics and mathematics.

We analyse the structure of solutions of Einstein theory and determines the number of independent parameters or degrees of freedom of the metrics and conjecture a quantum gravity model according to this number.

According to a topological analysis of emergence we define emergence as a topological property of finite physical/dynamical systems on compact manifolds and formulate the theory of ememrgence.

The so-called affine quantization is a trivial deformation of old quantization in a questionable manner. Recently Mr. Klauder and collaborator applied this method where the basics of physics and mathematics are trampled underfoot (1). Just as the actual invariant action integral is absent from which the Schroedinger equation should be derived accor...