A note on quantum field theories with a minimal length scale

2007/12/17 by Sabine Hossenfelder, S. Hossenfelder · 3 citations
Physics and Astronomy · #Asymptotic expansion #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Field (mathematics) #Geometry #Inverse #Length scale #Limit (mathematics) #Mathematical analysis #Mathematical physics #Noncommutative and Quantum Gravity Theories #Order (exchange) #Physics #Propagator #Pure mathematics #Quantum #Quantum field theory #Quantum gravity #Quantum mechanics #Scale (ratio) #Series (stratigraphy) #Theoretical physics #hep-th

paper · pdf · doi:10.1088/0264-9381/25/3/038003

published as Class.Quant.Grav.25:038003,2008

arxiv created 2007/12/17 · openalex publication_date 2008/01/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The aim of this note is to address the low energy limit of quantum field theories with a minimal length scale. The essential feature of these models is that the mininal length acts as a regulator in the asymptotic high energy limit which is incorporated through an infinite series of higher order derivatives. If one investigates a perturbative expansion in inverse powers of the Planck mass, one generically obtains extra poles in the propagator, and instabilities connected with the higher order derivative Lagrangian, which are however artifacts of truncating the series.

Citations

• THE MINIMAL LENGTH AND LARGE EXTRA DIMENSIONS
• On the problem of stability for higher-order derivative Lagrangian systems
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Higher-derivative Lagrangians, nonlocality, problems, and solutions

Cited by

• Free Motion of a Dirac Particle with a Minimum Uncertainty in Position
• Tests of quantum gravity-induced non-locality: Hamiltonian formulation of a non-local harmonic oscillator
• A new formulation of the initial value problem for nonlocal theories