Quantum Field
Theory
Quantum
Topodynamics
Diaa A Ahmed
Research Interests
Quantum
Topodynamics, Quantum Topology, M Theory, Quantum Supergravity
Theory, Gauge Unification of Fundamental Interactions, Gauge Field
Theory, Quantum Gravity, Quantum Computation, Quantum Theory of
the Mind.
"Quantum Topology" here means that the
quantum of action h generates a functional "quantum space" and
that the energy-momentum and space-time are dual coordinates that
live and get projected from that topological space which
represents the invariant arena in which physical interactions take
place. In quantum theory we have an abstract mathematical image of
that quantum manifold in the form of an antilinear-bilinear form;
the complete Dirac bracket,
< 0 | 0 >
Quantum space provides a consistent mathematical scheme to
incorporate both theory of relativity represented by a space-time
manifold and quantum mechanics represented by a quantum dynamical
variable that is non-commutative with the manifold. The manifold
and quantum dynamics are connected in a mathematical manner
similar to the way vectors and their dual vectors are connected in
the theory of functional spaces. The relativistic manifold is
extended into a quantum manifold that incorporates quantum
dynamics, and commutation relations define topological structures
in the quantum manifold.
"Quantum Topodynamics"
incorporates the gauge interactions into the structure of the
quantum manifold through introducing a proper topological group
structure on the fundamental set of the quantum space. A quantum
set is defined as the 2-fold infinite set of the dual coordinates
of the quantum space D and Q provided by the Fourier
representation. Then, we study the continuous mathematical
transformations on the set that generate a topological group with
a compact graded Lie manifold and gauge field (fibre bundle
structure of the quantum space).
We represent the
continuous mapping on the set as a logical operation to represent
the algebraic structure as an orthomodular structure. This
approach maps the structure of the group into properties of the
logic. This gives us an insight into quantum computation and a
criterion for the finiteness of functional integration on the
basis of the global properties of the functional space. An
immediate application to the central role played by the fibre
bundle structure in quantum computation is to attempt to construct
a quantum processor along the sructure of the fibre bundle. By
representing the fundamental operation as quantum interference and
reflecting the group structure in a matrix quantum interference
devise, this matrix processor will allow NxN gauge potentials to
act on the phases of N rays and the interference of these rays
will generate a continuous holographic output that represents the
topology of the quantum state being computed from the functional
integral of quantum topodynamics.
Articles Reviews
Abstracts of Articles
Physics/9812037
CERN
Abstract Physics/9812037 LANL
Quantum Topology LANL
Quantum Topodynamics LANL
Differential Topology in Quantum Space LANL
Gauge Theory of Gravitation LANL
Theory of The Quantum Space
The Dirac Quantum Field
Theory of the Functional Space
Quantum Dynamics of the Space
Quantum Topology
Preprints of Quantum Topodynamics
SLAC CERN
Preprints of Quantum Topology
SLAC CERN
Preprints of Quantum Space
SLAC CERN
Preprints of Topological Quantum Field
Theory SLAC CERN
Reference Pages
Development of Quantum Theory
Notes on Quantum Topology
Bookmarks "High Energy Physics Online"
Bookmarks "Field and Particle Theory"
Bookmarks "Culture Issues"
Search Engines & Web Tools
Physics WebSites
American Physical
Society
European Physical Society
American Association for Advancement of
Science
American Institute of Physics
arXiv.org
CERN Document Server
SLAC Library SPIRES Databases
Interactions
The Net Advance of Physics
Physics Central
PhysLINK
PhysNet
Physics World
String Theory Reviews
Symmetry
Mathematical Subject
Classification
Cartan's Corner
History of Mathematics
Contact Information
Diaa A Ahmed
e-mail:diahmed@yahoo.com