Landau Pole

In physics, the Landau pole or the Moscow zero is the momentum (or energy) scale at which the coupling constant (interaction strength) of a quantum field theory becomes infinite. Such a possibility was pointed out by the physicist Lev Landau and his colleagues The fact that coupling constants depend on the momentum (or length) scale is one of the basic ideas behind the renormalization group.

Landau poles appear in theories that are not asymptotically free, such as quantum electrodynamics (QED) or theory, i.e. a scalar field with a quartic interaction, such as may describe the Higgs boson. In these theories, the renormalized coupling constant grows with energy. A Landau pole appears when the coupling constant becomes infinite at a finite energy scale. In a theory intended to be complete, this could be considered a mathematical inconsistency. A possible solution is that the renormalized charge could go to zero as the cut-off is removed, meaning that the charge is completely screened by quantum fluctuations (vacuum polarization). This is a case of quantum triviality, which means that quantum corrections completely suppress the interactions in the absence of a cut-off.

Since the Landau pole is normally calculated using perturbative one-loop or two-loop calculations, it is possible that the pole is merely a sign that the perturbative approximation breaks down at strong coupling. Lattice field theory provides a means to address questions in quantum field theory beyond the realm of perturbation theory, and thus has been used to attempt to resolve this question. Numerical computations performed in this framework seems to confirm Landau's conclusion. Recent developments give a new insight into this problem.