Pair Production in Real Proper Time and Unitarity Without Borel Ambiguity

Abstract

The pair production of scalar particles in electromagnetic background fields is analyzed using real proper time formulation of 1-loop effective action. After explaining how real proper time formulation keeps unitarity of the particle creation process in an unambiguous way and discussing the (lack of) pair production in uniform (magnetic) electric backgrounds, we apply these ideas to general electric field backgrounds. Our approach is based on a recursive perturbative expansion of the proper time propagator $U(t)$ and we show how the pair production probabilities can be obtained from its singularities which arises upon a Pade summation of the expansion. We computed the pair production probabilities for general space or time dependent electric fields in locally constant approximation and showed they match with the well-known worldline instanton calculations of pulse and periodic backgrounds. Later, for one dimensional periodic electric and magnetic backgrounds, we showed how the WKB integrals appear in the classical limit. We linked both cases to specific WKB cycles in different spectral regions of the WKB problem and computed the WKB actions by evaluating the WKB integrals as well as by taking phase space integrals directly along Lefschetz thimbles. Finally, we explain the equivalence of our construction with exact WKB method in the classical limit by showing how the WKB cycles precisely contribute to the pair production process which is in complete agreement with our time dependent setting.

arXiv commentv2. Revised and extended version with new computational and conceptual results. 42 pages, 6 figures

References in corpus (34)

• Perturbative Quantum Field Theory in the String-Inspired Formalism
• Worldline Instantons and Pair Production in Inhomogeneous Fields
• Heisenberg-Euler Effective Lagrangians : Basics and Extensions
• Analytic Continuation Of Chern-Simons Theory
• Lorentzian Quantum Cosmology
• The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses
• Schwinger mechanism revisited
• Schwinger Pair Production via Instantons in Strong Electric Fields
• Uniform WKB, Multi-instantons, and Resurgent Trans-Series
• No smooth beginning for spacetime
• The Schwinger mechanism revisited
• Nonperturbative Ambiguities and the Reality of Resurgent Transseries
• Schwinger Pair Production in Electric and Magnetic Fields
• Improved Approximations for Fermion Pair Production in Inhomogeneous Electric Fields
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• Derivative Expansion of the Effective Action for QED in 2+1 and 3+1 dimensions
• Complex Worldline Instantons and Quantum Interference in Vacuum Pair Production
• Consequences of Dirac Theory of the Positron
• The Higher Derivative Expansion of the Effective Action by the String Inspired Method. Part II
• Borel Summation of the Derivative Expansion and Effective Actions
• Multidimensional Worldline Instantons
• Dynamically assisted Sauter-Schwinger effect in inhomogeneous electric fields
• Deconstructing zero: resurgence, supersymmetry and complex saddles
• Physical Resurgent Extrapolation
• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• Nonperturbative pair production in interpolating fields
• Path integration over closed loops and Gutzwiller's trace formula
• Uniformization and Constructive Analytic Continuation of Taylor Series
• On the Higher Loop Euler-Heisenberg Trans-Series Structure
• Lorentzian worldline path integral approach to Schwinger effect
• Multidimensional quantum tunneling in the Schwinger effect
• On Chebyshev Wells: Periods, Deformations, and Resurgence
• Quantum tunnelling from vacuum in multidimensions
• Recursive Generation of The Semi-Classical Expansion in Arbitrary Dimension