The Landau pole is a concept in quantum field theory referring to a hypothetical energy scale at which a coupling constant becomes infinite, meaning the strength of an interaction diverges. This signals a breakdown of the theory, as predictions become meaningless at that point.
The idea originated in studies of quantum electrodynamics (QED), where calculations show that the electromagnetic coupling constant (essentially the fine-structure constant) increases with energy. If extrapolated far enough, this increase leads to a point—the Landau pole—where the coupling becomes infinitely strong.
In practice:
- The Landau pole is thought to exist at an energy far beyond the Planck scale, so it has no observable consequences within the current range of experiments.
- Its existence implies that QED alone cannot be a complete theory at all energy scales and may need to be embedded in a more fundamental framework.
- Similar poles can arise in other field theories, suggesting limitations of perturbative methods or indicating the need for new physics.
Some theories, like quantum chromodynamics (QCD), avoid a Landau pole through behaviors like asymptotic freedom, where the coupling gets weaker at high energies.
The Landau pole highlights that even well-tested theories like QED may be effective rather than fundamental, and underscores the need for deeper, unified theories at extreme energy scales.