Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta

Details Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta

1994-05-10

arxiv.org/abs/hep-th/9405067v3

Physics

High Energy Physics

High Energy Physics - Theory

52 pages LATEX, DAMTP/93-33. Revised version now includes a chapter on the Poincare algebra and curvature as noncommutativity

Scientific paper

10.1007/BF01690456

A noncommutative geometric generalisation of the quantum field theoretical framework is developed by generalising the Heisenberg commutation relations. There appear nonzero minimal uncertainties in positions and in momenta. As the main result it is shown with the example of a quadratically ultraviolet divergent graph in $\phi^4$ theory that nonzero minimal uncertainties in positions do have the power to regularise. These studies are motivated with the ansatz that nonzero minimal uncertainties in positions and in momenta arise from gravity. Algebraic techniques are used that have been developed in the field of quantum groups.

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