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General arguments about combining gravity with quantum mechanics lead to the conclusion that Nature should have an absolute minimal length scale. A minimal length scale breaks dilation or scale symmetry. In this essay, we break dilation symmetry by modifying the virial operator, the generator of dilations. The construction of the modified virial operator is connected to an approach to solving the long standing and unsolved Riemann hypothesis with overtones to Weyl’s formulation of gauge theory.

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Minimal Length Scale in Quantum Gravity via Riemann and Weyl

  • 章节

  • 发表日期：

    2025年

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  • Erick Aiken,
  • Michael Bishop,
  • Douglas Singleton

摘要

General arguments about combining gravity with quantum mechanics lead to the conclusion that Nature should have an absolute minimal length scale. A minimal length scale breaks dilation or scale symmetry. In this essay, we break dilation symmetry by modifying the virial operator, the generator of dilations. The construction of the modified virial operator is connected to an approach to solving the long standing and unsolved Riemann hypothesis with overtones to Weyl’s formulation of gauge theory.