Landau pole
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| Landau pole | |
|---|---|
| Name | Landau pole |
| Field | Quantum field theory |
| Discovered | 1950s |
| Discoverer | Lev Landau |
| Related | Renormalization group, Quantum electrodynamics, Quantum chromodynamics, Perturbation theory |
Landau pole The Landau pole is a predicted divergence of a coupling constant at finite energy scale in certain quantum field theorys, implying a breakdown of perturbative description. It emerged in mid‑20th century discussions involving Lev Landau, Abram Ioffe, and contemporaries, and has influenced research at institutions such as CERN and Princeton University. The concept connects to work on the renormalization group, beta function, and high‑energy behavior in models studied at laboratories like SLAC and observatories such as Fermilab.
Introduction
The Landau pole concept appears when the renormalization group flow of a coupling hits a singularity at finite momentum, as found in early analyses by Lev Landau and collaborators. It is discussed alongside the beta function computations in perturbative expansions used in contexts including Quantum electrodynamics and model studies at Cambridge University and Moscow State University. The phenomenon raises questions about the ultraviolet completion pursued by programs at CERN, the Max Planck Society, and research groups influenced by Kenneth Wilson and Miguel Alcubierre.
Origin in Quantum Field Theory
Historically, Landau and colleagues analyzed the behavior of bare and renormalized charges in Quantum electrodynamics after developments by Paul Dirac and Richard Feynman. Using perturbation theory and renormalization techniques advanced by Gell-Mann–Low analysis and work at Harvard University, they identified a pole in the running coupling via the one‑loop beta function approximation. This result connected to formal studies by John Wheeler and debates involving researchers at Institute for Advanced Study and Steklov Institute about consistency of quantum field models. Subsequent elaborations by figures at Princeton University and Yale University extended these calculations to other gauge theories.
Examples in Specific Theories
In Quantum electrodynamics, perturbative evaluation of the beta function indicates a Landau pole at an astronomically high energy, a conclusion discussed in seminars at Oxford University and Columbia University. Scalar field theories such as the Phi^4 theory display triviality related to Landau pole behavior, explored in lattice studies at Brookhaven National Laboratory and DESY. Non‑abelian gauge theories like Quantum chromodynamics evade a Landau pole in the ultraviolet thanks to asymptotic freedom discovered by David Gross, Frank Wilczek, and David Politzer, work associated with MIT and Caltech. Models studied at Los Alamos National Laboratory and in conferences organized by International Centre for Theoretical Physics compare Abelian and non‑Abelian cases and examine examples like the O(N) model and Yukawa theory.
Physical Interpretations and Implications
A Landau pole can signal that a theory is only an effective description valid below some cutoff scale, a viewpoint adopted in effective field theory programs at Stanford University and UC Berkeley. It challenges the notion of a fundamental Abelian gauge theory, influencing ideas tied to the Standard Model and grand unified proposals discussed at KEK and Institute for Theoretical Physics (Utrecht). Debates at symposiums organized by Royal Society and American Physical Society have contrasted interpretations: the pole as pathology requiring new physics (as in proposals by Steven Weinberg) versus a mathematical artifact of perturbation theory emphasized by researchers at Perimeter Institute and University of Chicago.
Approaches to Resolution
Possible resolutions include embedding the theory in a larger framework such as grand unified theories explored at SLAC National Accelerator Laboratory and CERN, invoking asymptotic safety scenarios advocated by researchers connected to Imperial College London and Rudolf Peierls‑inspired circles, or nonperturbative completions studied using lattice methods pioneered at Trinity College Dublin and SISSA. Techniques from the functional renormalization group community at University of Heidelberg and nonperturbative resummation strategies developed in groups at Louisiana State University aim to remove or reinterpret the pole. Proposals involving new degrees of freedom at high energy have been pursued in collaborations involving Lawrence Berkeley National Laboratory and universities such as Johns Hopkins University.
Experimental and Observational Status
No direct experimental signal of a Landau pole exists, with high‑precision tests at LEP, Large Hadron Collider, and Tevatron constraining running couplings within accessible energy ranges. Collider programs at CERN and planned facilities like the Future Circular Collider would test extrapolations but cannot reach scales where a QED Landau pole is typically predicted. Precision atomic measurements and astrophysical observations analyzed by groups at Max Planck Institute for Astrophysics and NASA indirectly support the view that standard model couplings run as expected up to tested energies. The issue remains primarily theoretical, debated in workshops at International Centre for Theoretical Physics and colloquia at Princeton Plasma Physics Laboratory.