Quantum Fluctuations and Dynamical Chaos: An Effective Potential Approach

Abstract

We discuss the intimate connection between the chaotic dynamics of a classical field theory and the instability of the one-loop effective action of the associated quantum field theory. Using the example of massless scalar electrodynamics, we show how the radiatively induced spontaneous symmetry breaking stabilizes the vacuum state against chaos, and we speculate that monopole condensation can have the same effect in non-Abelian gauge theories.

12 pages, contribution to a special volume of ``Foundations in Physics'' commemorating L.C. Biedenharn (minor corrections)

References in corpus (5)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Vacuum Decay in Theories with Symmetry Breaking by Radiative Corrections
• Hamiltonian Dynamics of Yang-Mills Fields on a Lattice
• Lyapunov Exponent and Plasmon Damping Rate in Nonabelian Gauge Theories
• A Lattice Simulation of the SU(2) Vacuum Structure

Cited by in corpus (4)

• Manifestly scale-invariant regularization and quantum effective operators
• A "Helium Atom" of Space: Dynamical Instability of the Isochoric Pentahedron
• Accurate energy spectrum for the quantum Yang-Mills mechanics with nonlinear color oscillations
• Supersymmetry and Integrability in Planar Mechanical Systems