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

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

1996-02-15

arxiv.org/abs/hep-th/9602085v1

J.Math.Phys. 38 (1997) 1347-1372

Physics

High Energy Physics

High Energy Physics - Theory

LaTex, 32 pages

Scientific paper

10.1063/1.531814

We continue studies on quantum field theories on noncommutative geometric spaces, focusing on classes of noncommutative geometries which imply ultraviolet and infrared modifications in the form of nonzero minimal uncertainties in positions and momenta. The case of the ultraviolet modified uncertainty relation which has appeared from string theory and quantum gravity is covered. The example of euclidean $\phi^4$-theory is studied in detail and in this example we can now show ultraviolet and infrared regularisation of all graphs.

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