[Paper Review] Higgs Mechanism and Symmetry Breaking without Redundant Variables

Dieter Stoll, Michael Thies|ArXiv.org|Apr 12, 1995

Quantum Mechanics and Applications4 references3 citations

TL;DR

This paper reinterprets the Higgs mechanism in quantized gauge theories by eliminating redundant degrees of freedom via the canonical Weyl gauge formulation, showing that mass generation and symmetry breaking emerge without invoking gauge symmetry breaking. It identifies massless vector bosons in non-abelian models as signals of spontaneous global symmetry breaking, reinterpreting the physical photon as a Goldstone boson and clarifying distinctions between QED and the Georgi-Glashow model's displacement symmetries.

ABSTRACT

The Higgs mechanism is reconsidered in the canonical Weyl gauge formulation of quantized gauge theories, using an approach in which redundant degrees of freedom are eliminated. As a consequence, its symmetry aspects appear in a different light. All the established physics consequences of the Higgs mechanism are recovered without invoking gauge symmetry breaking. The occurence of massless vector bosons in non-abelian Higgs models is interpreted as signal of spontaneous breakdown of certain global symmetries. Characteristic differences between the relevant ``displacement symmetries'' of QED and the Georgi Glashow model are exhibited. Implications for the symmetry aspects of the electroweak sector of the standard model and the interpretation of the physical photon as Goldstone boson are pointed out.

Motivation & Objective

• To re-express the Higgs mechanism in a formulation that removes unphysical degrees of freedom using the canonical Weyl gauge.
• To clarify the role of symmetry breaking in non-abelian Higgs models without appealing to gauge symmetry breaking.
• To identify the origin of massless vector bosons as a signature of spontaneous global symmetry breaking.
• To analyze and contrast the displacement symmetries in QED and the Georgi-Glashow model.
• To reinterpret the physical photon in the electroweak sector as a Goldstone boson arising from spontaneous global symmetry breaking.

Proposed method

• Adopts the canonical Weyl gauge formulation to eliminate redundant degrees of freedom in quantized gauge theories.
• Uses a Hamiltonian approach to analyze the system without introducing unphysical fields.
• Identifies global symmetries whose spontaneous breaking leads to massless vector bosons in non-abelian models.
• Analyzes the structure of the Higgs potential and its vacuum expectation value in the absence of gauge-fixing artifacts.
• Compares the symmetry structures of QED and the Georgi-Glashow model through their respective displacement symmetries.
• Reinterprets the physical photon as a Goldstone boson associated with the spontaneous breaking of a global symmetry rather than a gauge symmetry.

Experimental results

Research questions

• RQ1 How can the Higgs mechanism be formulated without relying on redundant variables or gauge symmetry breaking?
• RQ2 What is the role of global symmetries in generating massless vector bosons in non-abelian Higgs models?
• RQ3 How do the displacement symmetries in QED differ from those in the Georgi-Glashow model?
• RQ4 Can the physical photon in the electroweak sector be understood as a Goldstone boson?
• RQ5 What are the implications of this formulation for the symmetry structure of the Standard Model's electroweak sector?

Key findings

• The Higgs mechanism and all its physical consequences are recovered without invoking gauge symmetry breaking.
• Massless vector bosons in non-abelian Higgs models are shown to arise from the spontaneous breaking of global symmetries, not gauge symmetry.
• The physical photon in the electroweak model is identified as a Goldstone boson associated with the spontaneous breaking of a global symmetry.
• The paper exhibits clear differences in the displacement symmetry structures between QED and the Georgi-Glashow model.
• The canonical Weyl gauge formulation successfully eliminates redundant degrees of freedom while preserving the physical content of the theory.
• The analysis provides a new perspective on the electroweak sector, where the Higgs mechanism is reinterpreted through global symmetry breaking rather than gauge symmetry breaking.