Weyl gauge-vector and complex dilaton scalar for conformal symmetry and its breaking

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• 作者：Hans C. Ohanian
• 关键词：Quantum gravity ; Conformal invariance ; Spontaneous symmetry breaking ; Weyl length transport
• 刊名：General Relativity and Gravitation
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：48
• 期：3
• 全文大小：461 KB
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• 作者单位：Hans C. Ohanian (1)
  
  1. Department of Physics, University of Vermont, Burlington, VT, 05405-0125, USA
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Relativity and Cosmology
  Differential Geometry
  Quantum Physics
  Astronomy, Astrophysics and Cosmology
  
• 出版者：Springer Netherlands
• ISSN：1572-9532

文摘

Instead of the scalar “dilaton” field that is usually adopted to construct conformally invariant Lagrangians for gravitation, we here propose a hybrid construction, involving both a complex dilaton scalar and a Weyl gauge-vector, in accord with Weyl’s original concept of a non-Riemannian conformal geometry with a transport law for length and time intervals, for which this gauge vector is required. Such a hybrid construction permits us to avoid the wrong sign of the dilaton kinetic term (the ghost problem) that afflicts the usual construction. The introduction of a Weyl gauge-vector and its interaction with the dilaton also has the collateral benefit of providing an explicit mechanism for spontaneous breaking of the conformal symmetry, whereby the dilaton and the Weyl gauge-vector acquire masses somewhat smaller than \(\textit{m}_\textit{P}\) by the Coleman–Weinberg mechanism. Conformal symmetry breaking is assumed to precede inflation, which occurs later by a separate GUT or electroweak symmetry breaking, as in inflationary models based on the Higgs boson. Keywords Quantum gravity Conformal invariance Spontaneous symmetry breaking Weyl length transport