Landau pole

This is sometimes called the Landau pole problem.

In 4 dimensions, φ theories have a Landau pole.

This property, called a Landau pole, made it plausible that quantum field theories were all inconsistent.

This phenomenon is usually called a Landau pole, and it defines the smallest length scale that a theory can describe.

A Landau pole appears when the coupling constant becomes infinite at a finite energy scale.

The latter singularity is the Landau pole.

If quantum electrodynamics were an exact theory, the fine structure constant would actually diverge at an energy known as the Landau pole.

In fact, the coupling apparently becomes infinite at some finite energy, resulting in a Landau pole.

In QED this gives rise to the phenomenon of the Landau pole.

This is the case when we have a Landau pole and for nonrenormalizable couplings like the Fermi interaction.

(See Landau pole for details and references.)

While the Standard Model is not entirely asymptotically free, in practice the Landau pole can only be a problem when thinking about the strong interactions.

It is this dependence that leads to the Landau pole mentioned earlier, and requires that the cutoff be kept finite.

If the latter has a Landau pole, then this fact is used in setting a "triviality bound" on the Higgs mass.

The problem of the Landau pole in QED is of pure academic interest.

This phenomenon was first noted by Lev Landau, and is called the Landau pole.

If this behavior persists at large couplings, this would indicate the presence of a Landau pole at finite energy, or quantum triviality.

In 1974, Gross, Politzer and Wilczek showed that another quantum field theory, quantum chromodynamics, does not have a Landau pole.

Solution of the Landau pole problem requires calculation of the Gell-Mann-Low function at arbitrary and, in particular, its asymptotic behavior for .

The Landau pole question is generally considered to be of minor academic interest for quantum electrodynamics because of the inaccessibly large momentum scale at which the inconsistency appears.

Asymptotically free theories become weak at short distances, there is no Landau pole, and these quantum field theories are believed to be completely consistent down to any length scale.

Alternatively, if the cutoff is allowed to go to infinity, the Landau pole can be avoided only if the renormalized coupling runs to zero, rendering the theory trivial.

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.

Alternatively, the field theory may be interpreted as an effective theory, in which the cutoff is not removed, giving finite interactions but leading to a Landau pole at some energy scale.

In a theory intended to represent a physical interaction where the coupling constant is known to be non-zero, Landau poles or triviality may be viewed as a sign of incompleteness in the theory.