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On quantum field theory with nonzero minimal uncertainties in positions and momenta. (English) Zbl 0872.58009

Summary: 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 regularization of all graphs.

MSC:

46L85 Noncommutative topology
46L87 Noncommutative differential geometry
81T99 Quantum field theory; related classical field theories
81Q99 General mathematical topics and methods in quantum theory
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