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F. Ghaboussi

Publications and source records attributed to F. Ghaboussi.

At least 19 recordsLinked to original sources
arXiv2021

A topological approach to renormalization and its geometrical, dimensional consequences

The necessity of renormalization arises from the infinite integrals which are caused by the discrepancy between the orders of differential and integral operators in the four dimensional QFTs. Therefore in view of the fact that finiteness and invariant properties of operators are their topological aspects, essential renormalization tools to extract finite invariant values from those infinities which are comparable with the experimental results, e. g. regularization, perturbation and radiative corrections follow some topological standards. In the second part we consider dimensional and geometrical consequences of topological approach to renormalization for the geometrical structure and degrees of freedom of renormalized theory. We show that regularization and renormalization of QED are performed only by certain restrictive dimensional conditions on QED fields. Further it is shown that in accord with our previous topological approach to renormalization of QED the geometrical evaluation of applied dimensional renormalization conditions and the appearance of anomalies refer to a reduction of number of degrees of freedom according to the reduced symmetry of QED. A conclusion concerning a comparison of our results with holographic principle models is also included.

physics.gen-ph↗
arXiv2021

On the fundamental structure of quantum mechanics

We show that there is no real difference between mathematical models of quantum mechanics and classical mechanics concerning integrable dynamical systems because the main difference between them results from their different interpretations.

physics.gen-ph↗
arXiv2003

A Two dimensional Model of Superconductivity

We present a two dimensional model of superconductivity where bosonization of fermions is described by topological fermion-boson duality. The model solves the discrepancy between theoretical and empirical values of penetration depth and explains the appearence of quantized vortex lines in supercunductors in accord with cyclotron motion of supercunducting electrons.

cond-mat.supr-con↗
arXiv2003

On the Stability of Yang-Mills Bundles over $S^4$

The stability of Yang-Mills bundles over the usual $S^4$ space-time manifold is investigated according to the topological methods. The necessary gauge- and topological invaraint criterion for the exsitence of the related critical points is defined. It is shown that according to this criterion there exists no critical point even for the action functional of the standard U(1) gauge theory of electrodynamics on a $S^4$ manifold in view of its topological structure and therefore such a theory can not be stable. We will discuss also a general consequence of this result according to which for a stable U(1) Yang-Mills theory over a compact 4-manifold, this manifold should possess some self consistent compact 2-manifold substructure. These results are also in agreement with the known very general result for the {\it structural stability} of dynamical systems.

hep-th↗
arXiv2003

Dimensional Structure of Space-Time

The dimensional structure of space-time is investigated according to physical and mathematical methods. We show that ther are various empirical and theoretical restrictions on the number of independent dimensions of space-time, consequently there is no physical and mathematical evidence for a space-time with four independent dimensions.

gr-qc↗
arXiv1999

On The Equivalence Of Four Dimensional And Two dimensional Field Theories

We investigate the dimensional, the dynamical and the topological structures of four dimensional Einstein and Yang-Mills theories. It is shown that these theories are constructed from two dimensional quantities, so that they possess always a distinguished two dimensional substructure. In this sense the four dimensional field theories are equivalent to related two dimensional field theories.

hep-th↗
arXiv1998

Foundation of The Two dimensional Quantum Theory of Gravity

The two dimensional substructure of general relativity and gravity, and the two dimensional geometry of quantum effect by black hole are disclosed. Then the canonical quantization of the two dimensional theory of gravity is performed. It is shown that the resulting uncertainty relations can explain black hole quantum effects. A quantum gravitational length is also derived which can clarify the origin of Planck length.

gr-qc↗
arXiv1998

On Quantum Mechanics

We discuss the axiomatic basis of quantum mechanics and show that it is neither general nor consistent, since its axioms are incompatible with each other and moreover it does not incorporate the magnetic quantization as in the cyclotron motion. A general and consistent system of axioms is conjectured which incorporates also the magnetic quantization.

quant-ph↗
arXiv1997

A Topological Approach to Quantum Electrodynamics

The physical reasons in favour of a two dimensional topological model of quantum electrodynamics are discussed. It is shown that in accord with this model there is a new uncertainty relation for photon which is compatible with QED.

cond-mat.mes-hall↗
arXiv1997

Uncertainty Relations for Two Dimensional Quantized Electromagnetic Potential

The canonical quantization of flux is performed. It is shown that according to the canonical flux quantization there must be a new uncertainty relation: $e ΔA_m . Δx_m \geq \hbar$ where $A_m$ and $Δx_m \geq l_B$ are the electromagnetic gauge potential, the position uncertainty and the magnetic length, respectively. Other arguments in favour of this uncertainty relation are also discussed.

quant-ph↗
arXiv1997

The Canonical Flux Quantization and IQHE(revised)

It is shown that the canonical flux quantization, which is described by the uncertainty relation on the phase space of the flux system, can result in the quantization of Hall-measures. Further it is shown that the polarization of this phase space, which is necessary for its quantization, results in the vanishing of longitudinal resistivity and conductivity. The equivalence between this approach and the topological approach to QHE is also discussed.

cond-mat.mes-hall↗
arXiv1997

A new uncertainty Relation (revised version)

We formulate according to the quantum mechanical uncertainty relation a new quantum electrodynamical uncertainty relation $Δ\breve{A} . Δl \sim \hbar/e$ where $\breve{A}$ and $Δl \geq l_B$ are the electromagnetic pure gauge potential, the position uncertainty and the magnetic length, respectively. Then, we show that the observed potential drops on the edge of QHE samples are varifications of this uncertainty relation, where the quantum potential drop of the relevant component of potential can be considered as its quantum uncertainty $Δ\breve{A}$.

cond-mat.mes-hall↗
arXiv1996

Quantum Cohomology And All That

We found a quantum cohomology/homology of quantum Hall effect which arises as the invariant property of the Chern-Simons theory of quantum Hall effect and showed that it should be equivalent to the quantum cohomology which arose as the invariant property of topological sigma models. This isomorphism should be related with an equivalence between the supersymmetric- and quantization structures in two dimensional models and/or with an equivalence between topological sigma models and the Chern-Simons theory by the methode of master equation.

hep-th↗
arXiv1996

On Quantum Cohomology

We discuss a general quantum theoretical example of quantum cohomology and show that various mathematical aspects of quantum cohomology have quantum mechanical and also observable significance.

hep-th↗