Conjecture on the Physical Implications of the Scale Anomaly

2005/10/20 by Christopher T. Hill, Hill, Christopher T. · 1 citation
Computer Science · Earth and Planetary Sciences · Physics and Astronomy · #Computational Physics and Python Applications #Cosmology and Gravitation Theories #Earth Systems and Cosmic Evolution #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Experiment (hep-ex) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #gr-qc #hep-ex #hep-ph #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/0510177

Invited talk delivered at the Santa Fe Institute on the Occasion of the Celebration of the 75th Birthday of Murray Gell-Mann. July 23, 2005

openalex publication_date 2005/10/20 · arxiv created 2005/10/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Murray Gell-Mann, after co-inventing QCD, recognized the interplay of the scale anomaly, the renormalization group, and the origin of the strong scale, Lambda_QCD. I tell a story, then elaborate this concept, and for the sake of discussion, propose a conjecture that the physical world is scale invariant in the classical, ℏ -> 0, limit. This principle has implications for the dimensionality of space-time, the cosmological constant, the weak scale, and Planck scale.

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