Models of Quantum Space Time: Quantum Field Planes

Quantum field planes furnish a noncommutative differential algebra Ω which substitutes for the commutative algebra of functions and forms on a contractible manifold. The data requirered in their construction come from a quantum field theory. The basic idea is to replace the ground field C of quantum planes by the noncommutative algebra A of observables of the quantum field theory. HUTMP 94-B335 hep-th/9403170 1 A picture of quantum space time We wish to compound a global space time, which is quantum, from local Lorentz frames. The physics in the local Lorentz frames shall be described by a special relativistic local quantum field theory on a classical space time of some dimension. To accomplish such a construction, we need to generalize the classical setup of general relativity which involves a classical space time manifold and a differential calculus and geometry on it [3]. Quantum field planes furnish a noncommutative differential algebra Ω which substitutes for the commutative algebra of functions and forms on a contractible manifold. The basic data to construct it come from a quantum field theory in the local Lorentz frame.