Heisenberg-Euler effective Lagrangian is recast as a dispersion integral with the quantum dilogarithm as kernel, its imaginary part given directly by the dilogarithm and its real part involving the modular dual.
Heisenberg-Euler Effective Lagrangians : Basics and Extensions
7 Pith papers cite this work. Polarity classification is still indexing.
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abstract
I present a pedagogical review of Heisenberg-Euler effective Lagrangians, beginning with the original work of Heisenberg and Euler, and Weisskopf, for the one loop effective action of quantum electrodynamics in a constant electromagnetic background field, and then summarizing some of the important applications and generalizations to inhomogeneous background fields, nonabelian backgrounds, and higher loop effective Lagrangians.
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Inhomogeneous background fields convert Borel poles in the effective action to branch points and introduce new ones, allowing resurgent extrapolation to recover non-perturbative information from perturbative input more accurately than WKB or locally constant approximations.
The free particle, harmonic oscillator, and inverted oscillator are unified as parabolic, elliptic, and hyperbolic realizations of the same conformal module, with explicit mappings between their states, coherent states, and scattering data via metaplectic rotations and Mellin transforms.
Constant electric fields in de Sitter require a tachyonic photon mass ~H, yielding finite positive Schwinger currents for massless fermions and scalars after on-shell renormalization.
The leading low-T correction to the two-loop Heisenberg-Euler Lagrangian is extracted from derivatives of the one-loop zero-T version via real-time formalism, then dressed with tadpoles and resummed to all loops.
Introductory lectures cover resurgent asymptotics using examples like the Airy function, nonlinear Stokes phenomenon, Heisenberg-Euler action, and resurgent continuation.
citing papers explorer
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Heisenberg-Euler and the Quantum Dilogarithm
Heisenberg-Euler effective Lagrangian is recast as a dispersion integral with the quantum dilogarithm as kernel, its imaginary part given directly by the dilogarithm and its real part involving the modular dual.
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Resurgence of the Effective Action in Inhomogeneous Fields
Inhomogeneous background fields convert Borel poles in the effective action to branch points and introduce new ones, allowing resurgent extrapolation to recover non-perturbative information from perturbative input more accurately than WKB or locally constant approximations.
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The Free Particle--Oscillator--Inverted Oscillator Triangle: Conformal Bridges, Metaplectic Rotations and $\mathfrak{osp}(1|2)$ Structure
The free particle, harmonic oscillator, and inverted oscillator are unified as parabolic, elliptic, and hyperbolic realizations of the same conformal module, with explicit mappings between their states, coherent states, and scattering data via metaplectic rotations and Mellin transforms.
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Classical constant electric fields and the Schwinger effect in de Sitter
Constant electric fields in de Sitter require a tachyonic photon mass ~H, yielding finite positive Schwinger currents for massless fermions and scalars after on-shell renormalization.
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Leading low-temperature correction to the Heisenberg-Euler Lagrangian
The leading low-T correction to the two-loop Heisenberg-Euler Lagrangian is extracted from derivatives of the one-loop zero-T version via real-time formalism, then dressed with tadpoles and resummed to all loops.
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Introductory Lectures on Resurgence: CERN Summer School 2024
Introductory lectures cover resurgent asymptotics using examples like the Airy function, nonlinear Stokes phenomenon, Heisenberg-Euler action, and resurgent continuation.
- Euler-Heisenberg actions in higher dimensions