## 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.

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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

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

Development of Quantum Theory

Notes on Quantum Topology

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