Past and future blurring at fundamental length scale

Abstract

We obtain the $\kappa$-deformed versions of the retarded and advanced Green functions and show that their causality properties are blurred in a time interval of the order of a length parameter $q=1/(2\kappa )$. The functions also indicate a smearing of the light cone. These results favor the interpretation of $q$ as a fundamental length scale below which the concept of a point in spacetime should be substituted by the concept of a fuzzy region of radius $q$, as proposed long ago by Heisenberg.

Essentially, this is the version published in the Phys. Rev. Lett. 105, 211601 (2010). It has 4 pages and contains 2 figures

References in corpus (15)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Lorentz invariance with an invariant energy scale
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Modern tests of Lorentz invariance
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Generalized Lorentz invariance with an invariant energy scale
• D-branes and the Noncommutative Torus
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Doubly-Special Relativity: First Results and Key Open Problems
• Strings in Background Electric Field, Space/Time Noncommutativity and A New Noncritical String Theory
• General Properties of Noncommutative Field Theories
• Locality, Causality and Noncommutative Geometry

Cited by in corpus (4)

• Pauli-Jordan Function and Scalar Field Quantization in $\kappa$-Minkowski Noncommutative Spacetime
• Light Cone in a Quantum Spacetime
• Quantum causality in $\kappa$-Minkowski and related constraints
• Scaling Transformation for Nonlocal Interactions