Quantization of charged fields in the presence of critical potential steps

Abstract

QFT approaches elaborated for treating quantum effects in time-dependent external electric fields are not directly applicable to time-independent nonuniform electric fields that are given by a step potential and their generalization for the such potentials was not sufficiently developed. Such fields can also create particles from the vacuum, the Klein paradox being closely related to this process. We believe that the present work presents a consistent solution of the latter problem. Quantizing the Dirac and scalar fields with time independent backgrounds, we have found in- and out-creation and annihilation operators that allow one to have particle interpretation of the physical system under consideration. To justify the proposed identification, we have performed a detailed mathematical and physical analysis of solutions of the corresponding relativistic wave equations with a subsequent QFT analysis. We elaborated a nonperturbative technique that allows one to calculate all characteristics of zero-order processes such scattering, reflection, and electron-positron pair creation, and to calculate Feynman diagrams that describe all characteristics of processes with interaction between the in-, out-particles and photons. These diagrams have formally the usual form, but contain special propagators. Expressions for these propagators in terms of in- and out-solutions are presented. We apply the elaborated approach to two popular exactly solvable cases: to the Sauter potential and to the Klein step.

58 pages, 3 figures, misprints corrected, version accepted for publication in Physical Review D

References in corpus (24)

• The electronic properties of graphene
• Chiral tunneling and the Klein paradox in graphene
• Andreev reflection and Klein tunneling in graphene
• Quantum interference and Klein tunneling in graphene heterojunctions
• Colloquium: The transport properties of graphene: An introduction
• The Unruh effect and its applications
• Selective transmission of Dirac electrons and ballistic magnetoresistance of \textit{n-p} junctions in graphene
• Evidence of Klein tunneling in graphene p-n junctions
• Dirac Fermions in Solids - from High Tc cuprates and Graphene to Topological Insulators and Weyl Semimetals
• Dynamically assisted Schwinger mechanism
• Worldline Instantons II: The Fluctuation Prefactor
• Quantum simulation of the Klein paradox with trapped ions
• The Schwinger mechanism and graphene
• Improved Approximations for Fermion Pair Production in Inhomogeneous Electric Fields
• On the Instability of Global de Sitter Space to Particle Creation
• Consequences of Dirac Theory of the Positron
• Multidimensional Worldline Instantons
• Dirac fermions in strong electric field and quantum transport in graphene
• Modeling Klein tunneling and caustics of electron waves in graphene
• Gutzwiller's Trace Formula and Vacuum Pair Production
• Probing the quantum vacuum with ultra intense laser pulses
• Exact Pair Production Rate for a Smooth Potential Step
• A few more comments on secularly growing loop corrections in strong electric fields
• Probing Klein tunneling through quantum quenches

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• Regularization, renormalization and consistency conditions in QED with x-electric potential steps
• Vacuum instability in a constant inhomogeneous electric field. A new example of exact nonperturbative calculations
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• Unitarity and vacuum deformation in QED with critical potential steps
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• In- and out-states of scalar particles confined between two capacitor plates
• Short-distance Schwinger-mechanism and chiral symmetry
• Particle creation in cosmological space-time by a time-dependent electric field
• Vacuum instability in QED with an asymmetric x-step. New example of exactly solvable case
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• Dynamically assisted pair production in subcritical potential step and particle--anti-particle interpretations
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