Quantum Hall Effect and Chaotic Motion in Phase Space

We discuss the relation between the Quantum Hall behaviour of charged carriers and their chaotic motion in phase space. It is shown that the quantum Hall diagram is comparable with the stepped diagram in phase space of a chaotic motion.Comment: Late

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.Comment: 9 pages, latex, revised version

Uncertainty Relation For Quantized Magnetic Fields and The Quantum Hall Effect

We discuss a model where the relation between Hall potential $A_H$ = and gate potential $A_G$, which is manifested by the stepped QHE = curve, is described by an uncertainty relation $\Delta A_H . = \Delta A_G =3D B(\hbar/e)$.Comment: Latex, 5 pages (revised version

The Edge Currents in IQHE

It is shown that an observed length in the potential drops across IQHE samples is a universal length for a given magnetic field strength which has the magnitude equal to the reciprocal magnitude of magnetic length and which results from the quantum mechanical uncertainty relation in presence of magnetic field. The analytic solution of Ohm's equation for the potential in Corbino sample in IQHE is also given.Comment: 6 Pages, Late

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.Comment: 24 page

On Experimental Evidence of Uncertainty of Quantized Electromagnetic Potential from QHE

It is shown that the observed potential drops on QHE samples can be considered as a realization of uncertainty relation for the quantized two dimensional electromagnetic potential.Comment: Latex, 7 page

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.Comment: 13 pages, Latex, The paper is revise

A Model Of The Integer Quantum Hall Effect

We discuss a model for the integer quantum Hall effect which is based on a Schroedinger-Chern-Simons-action functional for a non-interacting system of electrons in an electromagnetic field on a mutiply connected manifold. In this model the integer values of the Hall conductivity arises in view of the quantization of the Chern-Simons-action functional for electromagnetic potential.Comment: Late

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.Comment: Latex, 27 page

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.Comment: Late