On Restricted Weyl Symmetry

Abstract

We discuss the physics of a restricted Weyl symmetry in a curved space-time where a gauge parameter $\Omega (x)$ of Weyl transformation satisfies a constraint $\square \Omega =0$. First, we present a model of QED where we have a restricted gauge symmetry in the sense that a $U(1)$ gauge parameter $\theta (x)$ obeys a similar constraint $\square \theta =0$ in a flat Minkowski space-time. Next, it is precisely shown that a global scale symmetry must be spontaneously broken at the quantum level. Finally, we discuss the origin of the restricted Weyl symmetry and show that its symmetry can be derived from a full Weyl symmetry by taking a gauge condition $R=0$ in the BRST formalism.

12 pages

References in corpus (9)

• Invariant Variation Problems
• Quantum scale invariance, cosmological constant and hierarchy problem
• Fake Conformal Symmetry in Conformal Cosmological Models
• Manifestly scale-invariant regularization and quantum effective operators
• Restricted Weyl invariance in four-dimensional curved spacetime
• Fake Conformal Symmetry in Unimodular Gravity
• Generating Einstein gravity, cosmological constant and Higgs mass from restricted Weyl invariance
• Critical gravity from four dimensional scale invariant gravity
• Planck scale from broken local conformal invariance in Weyl geometry

Cited by in corpus (7)

• Quantum Scale Invariant Gravity with de Donder Gauge
• BRST Formalism of Weyl Conformal Gravity
• Quadratic Gravity and Restricted Weyl Symmetry
• Higgs Potential from Weyl Conformal Gravity
• Restricted Weyl Symmetry and Spontaneous Symmetry Breakdown of Conformal Symmetry
• Quantum Theory of Weyl Invariant Scalar-tensor Gravity
• Critical reassessment of the restricted Weyl symmetry