Quantum diffusion of magnetic fields in a numerical worldline approach

Abstract

We propose a numerical technique for calculating effective actions of electromagnetic backgrounds based on the worldline formalism. As a conceptually simple example, we consider scalar electrodynamics in three dimensions to one-loop order. Beyond the constant-magnetic-field case, serving as a benchmark test, we analyze the effective action of a step-function-like magnetic field -- a configuration that is inaccessible to derivative expansions. We observe magnetic-field diffusion, i.e., nonvanishing magnetic action density at space points near the magnetic step where the classical field vanishes.

15 pages, 3 figures, v2: numerical analysis in Sect.3 improved, references added, typos corrected, version to appear in NPB

References in corpus (1)

• Quantum Energies of Interfaces

Cited by in corpus (61)

• Worldline Instantons and Pair Production in Inhomogeneous Fields
• Heisenberg-Euler Effective Lagrangians : Basics and Extensions
• Worldline Instantons II: The Fluctuation Prefactor
• Casimir Effect on the Worldline
• New Strong-Field QED Effects at ELI: Nonperturbative Vacuum Pair Production
• Casimir effect for curved geometries: PFA validity limits
• Schwinger mechanism revisited
• Worldline algorithms for Casimir configurations
• Pair production in inhomogeneous fields
• Approaches to the sign problem in lattice field theory
• Schwinger Pair Production in Electric and Magnetic Fields
• A Twisted Kink Crystal in the Chiral Gross-Neveu model
• Casimir edge effects
• Improved Approximations for Fermion Pair Production in Inhomogeneous Electric Fields
• Functional Determinants in Quantum Field Theory
• Loops and loop clouds - a numerical approach to the worldline formalism in QED -
• Electron-Positron Pair Production in Space- or Time-Dependent Electric Fields
• Quantum Reflection as a New Signature of Quantum Vacuum Nonlinearity
• Critical Schwinger pair production
• Fermion-induced quantum action of vortex systems
• Quantum mechanical path integrals in the first quantised approach to quantum field theory
• Discrete worldline instantons
• Scalar heat kernel with boundary in the worldline formalism
• Quantum energies with worldline numerics
• Quantum effective actions from nonperturbative worldline dynamics
• A curvature bound from gravitational catalysis
• Interplay between geometry and temperature for inclined Casimir plates
• Photon merging and splitting in electromagnetic field inhomogeneities
• Vacuum polarization tensor in inhomogeneous magnetic fields
• Fermionic Vacuum Energy from a Nielsen-Olesen Vortex
• Large orders in strong-field QED
• Quantum Corrections to Soliton Energies
• On the Vacuum energy of a Color Magnetic Vortex
• Geothermal Casimir phenomena for the sphere-plate and cylinder-plate configurations
• Worldline Monte Carlo for fermion models at large N_f
• Edges and Diffractive Effects in Casimir Energies
• The worldline approach to helicity flip in plane waves
• The Euler-Heisenberg Lagrangian beyond one loop
• Worldline instantons for nonlinear Breit-Wheeler pair production and Compton scattering
• External Fields as a Probe for Fundamental Physics
• Geothermal Casimir Phenomena
• Propagator from Nonperturbative Worldline Dynamics
• Determinant Calculations Using Random Walk Worldline Loops
• Born-series approach to the calculation of Casimir forces
• Integral representations combining ladders and crossed-ladders
• New Techniques for Worldline Integration
• Integral transforms of the quantum mechanical path integral: hit function and path averaged potential
• Worldline formalism for a confined scalar field
• Casimir Interactions between Magnetic Flux Tubes in a Dense Lattice
• On the Yang-Mills two-loop effective action with wordline methods
• Landau Levels of Scalar QED in Time-Dependent Magnetic Fields
• Geometry of spin-field coupling on the worldline
• Full mass range analysis of the QED effective action for an O(2)xO(3) symmetric field
• Applications of the worldline Monte Carlo formalism in quantum mechanics
• Strong magnetic field asymptotic behaviour for the fermion-induced effective energy in the presence of a magnetic flux tube
• On the Landau Ginzburg theory of MAG projected SU(2) lattice gauge theory
• Monte Carlo generation of localised particle trajectories
• Extra-Dimensions effects on the fermion-induced quantum energy in the presence of a constant magnetic field
• In-in worldline formalism in pair creating fields
• New asymptotic techniques for the partial wave cut-off method for calculating the QED one loop effective action
• Worldline Path Integrals for Gauge Fields and Quantum Computing