Magnetic Reconnection Picture of Electron–Positron Pair Production

1. Phenomenological Review and Problem Statement

In the standard quantum electrodynamics (QED) framework, high-energy photon-induced electron–positron pair production near an atomic nucleus is described as a canonical Feynman vertex process:

• An incoming photon line “splits” into an electron line and a positron line in the presence of the external field of a heavy nucleus;

• The nucleus absorbs a tiny recoil momentum to satisfy energy–momentum conservation;

• This is often supplemented by the textbook narrative of “vacuum fluctuations + external field promoting virtual pairs on-shell.”

This formulation is highly successful for cross-section calculations and numerical predictions. However, it largely sidesteps a deeper question:

In the actual spacetime field structure,
how does the combination of the incident electromagnetic energy and the static nuclear electromagnetic field
undergo a specific topological reorganization
to form two stable field configurations carrying definite charge and spin—the electron (e−) and positron (e+)?

Natural Quantum Theory (NQT) treats electrons and positrons as stable electromagnetic–topological vortex structures, while high-energy photons are finite-sized topological modes of the electromagnetic field. Under this ontological picture, pair production is naturally reinterpreted as:

A magnetic reconnection–type event occurring in the strong field near the nucleus:
the incident photon’s topological mode couples with the high-shear region of the nuclear field;
within a microscopic domain dominated by vacuum polarization and nonlinear effects,
field lines undergo violent breaking and reconnecting,
ultimately restructuring into two oppositely charged, chirally opposed topological vortices—electron and positron.

Below, we present a self-consistent field-topological evolution scenario within the NQT framework.

1. Initial State: Finite-Sized Photon Mode and Strong Nuclear Field

(1) Photon as a finite-scale electromagnetic topological mode

In NQT, the photon is no longer viewed as an infinitely extended plane wave, but as a localized electromagnetic pulse/wavepacket possessing:

• Finite transverse width and longitudinal extent;

• Internal circulation or helical structure (e.g., in energy flow or phase winding);

• A stable propagating mode carrying quantized energy and momentum.

This mode is an eigenmode of the Maxwell field under specific boundary and topological conditions, exhibiting well-defined field-line and energy-flow topology.

(2) Coulomb field of a heavy nucleus as a strongly sheared background medium

The electrostatic field around a heavy nucleus is extremely intense; when combined with possible magnetic dipole components, it features:

• Electromagnetic field lines sharply bent and densely packed over very short spatial scales;

• Significant vacuum polarization, rendering the effective electromagnetic medium nonlinear and anisotropic;

• Geometrically, a “highly curved” electromagnetic region—effectively a potential topological shear layer.

(3) Incident configuration: photon entering the strong-field shear zone

A high-energy photon approaches the nucleus along a trajectory. Its intrinsic electric (Eγ) and magnetic (Bγ) fields superpose onto the background nuclear fields (EN,BN), creating in a small region:

• Strong shear in field directions, locally approaching anti-parallel alignment;

• Field strengths exceeding the threshold for triggering vacuum polarization and nonlinear corrections;

• Partial refraction, deceleration, and trapping of the photon’s energy-flow lines.

This microscopic region becomes the site of topological “magnetic reconnection.”

1. Magnetic Reconnection–Type Topological Reorganization: From Photon Mode to e−e+ Vortices

(1) Breakup of the original photon topological mode

In ideal linear Maxwell theory, electromagnetic field-line topology is strictly “frozen-in.”
However, under extreme fields, vacuum polarization and nonlinear terms effectively introduce a “finite diffusion layer,” enabling:

• Stretching and twisting of the photon’s internal phase-flow lines and energy loops within the shear zone;

• Local emergence of strongly anti-parallel E and B configurations, analogous to the X-point structure in plasma magnetic reconnection;

• Loss of stability in the originally singly connected topological mode, allowing it to fragment.

(2) Field-line breaking and reconnection: generation of two oppositely chiral vortices

Within this localized “topological diffusion layer,” electric and magnetic field lines undergo a brief breaking–reconnection event:

• Part of the original photon energy-flow lines detach from and reconnect with nuclear field lines;

• Two geometrically closed, topologically nontrivial field-vortex bundles emerge;

These vortices exhibit opposite chirality and circulation directions, corresponding to the future electron and positron:

• One vortex’s internal circulation and flux structure defines negative charge and a specific spin orientation;

• The other realizes opposite flux orientation and chirality, corresponding to positive charge and opposite spin.

This process can be analogized as:

A single topologically neutral loop of circulation being “torn apart by shear and nonlinearity into two oppositely twisted knots,”
each of which self-consistently closes—under the joint constraints of field equations and boundary conditions—into a stable charged topological vortex.

(3) Emergence of charge: splitting and locking of flux structures

In NQT’s topological intuition, electric charge is associated with certain field-flux invariants. In pair production:

• The initial vacuum state has net zero charge, corresponding to a “topologically neutral” closed-field configuration;

• During reconnection, this closed flux structure is split into two segments;

• Their endpoints (or localized twist cores) become locked into the two newly formed vortices upon re-closure.

Consequently:

• One vortex exhibits net negative charge (electron);

• The other exhibits net positive charge (positron);

• Total charge remains conserved (net zero).

This parallels classical magnetic reconnection—“topology change + energy release”—except here the reconnecting entities are generalized electromagnetic–topological flux structures.

(4) Realization of energy–momentum conservation

From an energy–momentum perspective, the entire process is self-consistent:

• The incident photon energy Eγ, together with local energy from the nuclear field, supplies:

• The rest mass energy 2mc2 of the two massive vortex structures;

• Their kinetic energy and relative momentum;

• Possible residual radiation or minor reshaping of the nuclear field;

• The nucleus acquires a tiny recoil, ensuring total four-momentum conservation.

The reconnection zone serves merely as the geometric arena for “energy–topology reorganization,” while conservation laws are rigorously upheld through the coupled evolution of fields and sources.

1. Post-Reconnection: Electron and Positron as Stable Topological Vortices

After reconnection, the two newborn vortices are accelerated and separated by Lorentz forces in the nuclear field:

• At larger distances, they are detected as nearly point-like particles:

• Their trajectories bend in accordance with classical equations of motion for charged particles in external fields;

• Yet in the NQT picture, this is because their internal topological scale is far below observational resolution:

Each “particle” is fundamentally a stable electromagnetic–topological vortex with finite size and energy distribution;
its charge, spin, and magnetic moment are geometric/topological attributes of its internal field-line structure.

From a topological standpoint:

The essence of pair production is the transformation—via a localized topological reconnection—
of a “high-energy radiative topological mode + static nuclear field structure”
into “two stable charged field-vortex modes.”

1. Relation to Standard QED and Prospects for Further Development

This NQT–magnetic reconnection picture is compatible with, not contradictory to, standard QED:

• At the computational level:
  Feynman diagrams provide an algebraic encoding and perturbative expansion of the topological reconnection process;
  amplitudes and cross sections correspond to weighted sums over “all possible reconnection pathways.”

• At the ontological level:
  QED operates in operator and particle Fock space, deliberately avoiding questions about field morphology;
  NQT seeks to answer: What do these operator processes “look like” in continuous field topology?

Three promising directions for further development:

(a) Systematization of topological illustrations

• Develop standardized schematic diagrams of the sequence:
  photon incidence → nuclear field shear → topological reconnection → paired vortex formation;

• Explicitly depict the reconnection of electric field lines, magnetic field lines, and energy-flow lines;

• Provide intuitive visualizations for readers and geometric references for future numerical simulations.

(b) Model equations based on effective actions

• Employ the Heisenberg–Euler effective Lagrangian to describe nonlinear corrections to Maxwell’s equations in strong fields;

• Identify regions and conditions (e.g., when field invariants F=B2−E2/c2 and G=E⋅B exceed thresholds) that permit topological change;

• Explore whether such effective equations admit numerical or approximate analytical solutions resembling vortex-pair creation.

(c) Correspondence table with Feynman structures

• Map conceptual elements:

• Incident photon mode ↔ incoming photon line;

• Reconnection zone ↔ vertex + external nuclear line;

• Two vortices ↔ outgoing electron and positron lines;

• Establish a step-by-step correspondence between “topological reconnection stages” and “Feynman diagram components,”
  showing how NQT provides a physical-geometric interpretation of QED amplitudes without compromising their precision.

In this sense, pair production is no longer merely “an operator event at a vertex,” but rather:

A continuous electromagnetic field, under extreme shear in a strong background,
undergoing a brief yet violent topological reconnection,
thereby reorganizing radiative energy and static field structure
into two stable charged vortices—
the electron and the positron.