The Electron's Charge as an Emergent Property of Internal Field Dynamics

The Electron's Charge as an Emergent Property of Internal Field Dynamics

In conventional quantum field theory (QFT), the electron is modeled as a point-like particle with intrinsic, immutable properties: mass, spin, and electric charge. However, emerging theoretical perspectives suggest that these observable features—particularly electric charge—may instead arise from deeper dynamical behavior within field space.

The electron is a spin-1/2 fermion, described by a four-component Dirac spinor:

\[ \psi = \begin{pmatrix} \psi_L \\ \psi_R \end{pmatrix} \]

Here, \( \psi_L \) and \( \psi_R \) are the left- and right-chiral components of the electron field. In the Standard Model, these components are not symmetrical in their interactions. The left-chiral component couples to the weak force via the SU(2)_L symmetry, while the right-chiral component does not. Mass arises through a Yukawa interaction with the Higgs field:

\[ \mathcal{L}_\text{Yukawa} = -y_e \bar{L}_e H e_R + \text{h.c.} \]

This term couples the left-chiral doublet \( L_e = (\nu_e, e_L)^T \) to the right-chiral singlet \( e_R \), mediated by the Higgs field \( H \). After spontaneous symmetry breaking, the Higgs acquires a vacuum expectation value, mixing these chiral states and generating mass for the electron. This mass-generating mechanism induces a continual oscillation in field space between \( \psi_L \) and \( \psi_R \).

At the same time, the electron's spin-1/2 nature introduces a topological twist: its quantum state requires a 720-degree rotation to return to its original configuration. This behavior is not just an artifact of representation; it is rooted in the geometry of spinor fields, which live in the double cover of the rotation group SU(2). A 360-degree rotation induces a phase shift:

\[ \psi \rightarrow -\psi \]

Only a full 720-degree rotation restores the field to its initial state:

\[ \psi \rightarrow -(-\psi) = \psi \]

This phase evolution implies that the electron possesses a non-trivial internal geometry—one that evolves cyclically and is sensitive to orientation in field space. When considered together with the chirality-mixing process driven by the Higgs field, this suggests that the electron is not a static object, but a dynamically oscillating entity in a complex field manifold.

From this perspective, the property we identify as electric charge may be the external projection of this internal behavior. The electron's coupling to the electromagnetic field—via the U(1)_EM gauge symmetry—could be interpreted as arising from a deeper phase structure or internal circulation of the spinor field. In this view, charge is not simply "carried" by the electron, but rather emerges from its phase rotation, chirality dynamics, and synchronization with vacuum fields.

This interpretation is compatible with ideas in topological quantum field theory, where charges and conserved quantities often arise from geometric or phase structures. It also aligns with views in which the vacuum is not empty, but a structured medium with properties (such as permittivity and permeability) that guide and stabilize field interactions. The quantization of charge may then reflect a topologically stable phase mode within this structured vacuum.

Conclusion

The 720-degree spin symmetry of the electron, combined with its chirality-dependent mass and weak interactions, strongly suggests that charge is not a primitive trait, but an emergent feature of internal field rotation. This view provides both a geometric and dynamical explanation for why charge appears quantized, invariant, and always associated with specific field behaviors.

References and Further Reading

• Frankel, T. (2011). The Geometry of Physics: An Introduction. Cambridge University Press.
• Peskin, M.E. & Schroeder, D.V. (1995). An Introduction to Quantum Field Theory. Addison-Wesley.
• Sakurai, J.J. (1994). Advanced Quantum Mechanics. Pearson.
• Carroll, S. (2019). Spacetime and Geometry: An Introduction to General Relativity. Cambridge University Press.
• Spinors and Geometry in QFT – arXiv:hep-th/9411037
• Wikipedia: Spin-½
• Topological Charge Quantization and Spinor Geometry – arXiv:1810.11077