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

1996/02/15 by Achim Kempf · 3 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th #math.QA #q-alg

paper · pdf · doi:10.1063/1.531814

published as J.Math.Phys. 38 (1997) 1347-1372 · LaTex, 32 pages

arxiv created 1996/02/15 · openalex publication_date 1997/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

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 ϕ⁴-theory is studied in detail and in this example we can now show ultraviolet and infrared regularisation of all graphs.

Citations

• Quantum Fields in Curved Space
• Quantum group gauge theory on quantum spaces

Cited by

• Path integrals with generalized Grassmann variables
• Quantum dynamics of the Taub universe in a generalized uncertainty principle framework
• Noncommutative approach to the cosmological constant problem
• Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework