Finite Field Theory on Noncommutative Geometries

Abstract

The propagator is calculated on a noncommutative version of the flat plane and the Lobachevsky plane with and without an extra (euclidean) time parameter. In agreement with the general idea of noncommutative geometry it is found that the limit when the two `points' coincide is finite and diverges only when the geometry becomes commutative. The flat 4-dimensional case is also considered. This is at the moment less interesting since there has been no curved case developed with which it can be compared.

38pages, Latex2e, improved presentation

References in corpus (5)

• The quantum structure of spacetime at the Planck scale and quantum fields
• Noncommutative Geometry of the h-deformed Quantum Plane
• The Geometry of a $q$-Deformed Phase Space
• Quantum Mechanics on the h-deformed Quantum Plane
• Quantum Lobachevsky Planes

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• Non-Relativistic Non-Commutative Field Theory and UV/IR Mixing
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