An alternative to the gauge theoretic setting

TL;DR

This paper proposes a new string-like localization approach to gauge theories that preserves the Hilbert space structure and offers a deeper understanding of the Higgs mechanism, contrasting with traditional pointlike formulations.

Contribution

It introduces an intrinsic quantum approach using modular localization, replacing pointlike potentials with string-like localized potentials, and revisits the Higgs mechanism from this perspective.

Findings

String localization maintains Hilbert space positivity.

Interacting matter fields become string-generated and nonlocal.

Reinterpretation of the Higgs mechanism as a screening process.

Abstract

The standard formulation of gauge theories results from the Lagrangian (functional integral) quantization of classical gauge theories. A more intrinsic qunantum theoretical access in the spirit of Wigner's representation theory shows that there is a fundamental clash between the pointlike localization of zero mass (vector, tensor) potentials and the Hilbert space (positivity, unitarity) structure of QT. The quantization approach has no other way than to stay with pointlike localization and sacrifice the Hilbert space whereas the approach build on the intrinsic quantum concept of modular localization keeps the Hilbert space and trades the conflict creating pointlike generation with the tightest consistent localization:: semiinfinite spacelike string localization. Whereas these potentials in the presence of interactions stay quite close to associated pointlike field strength, the interacting matter fields to which they are coupled bear the brunt of the nonlocal aspect in that they are string.generated in a way which cannot be undone by any differentiation. The new stringlike approach to gauge theory also revives the idea of a Schwinger-Higgs screening mechanism as a deeper and less metaphoric description of the Higgs spontaneous symmetry breaking and its accompanying tale about "God's particle" and its mass generation for all other particles.