When physics is expressed in a way that is independent of local choices of unit systems, Riemannian geometry is replaced by conformal geometry. Moreover masses become geometric, appearing as Weyl weights of tractors (conformal multiplets of fields necessary to keep local unit invariance manifest). The relationship between these weights and masses is through the scalar curvature. As a consequence mass terms are spacetime dependent for off-shell gravitational backgrounds, but happily constant for physical, Einstein manifolds. Unfortunately this introduces a naturalness problem because the scalar curvature is proportional to the cosmological constant. By writing down tractor stress tensors (multiplets built from the standard stress tensor and its first and second derivatives), we show how back-reaction solves this naturalness problem. We also show that classical back-reaction generates an interesting potential for scalar fields. We speculate that a proper description of how physical systems couple to scale, could improve our understanding of naturalness problems caused by the disparity between the particle physics and observed, cosmological constants. We further give some ideas how an ambient description of tractor calculus could lead to a Ricci-flat/CFT correspondence which generalizes the AdS side of Maldacena's duality to a Ricci-flat space of one higher dimension.

Local unit invariance, back-reacting tractors and the cosmological constant problem / Roberto Bonezzi; Olindo Corradini; Andrew Waldron. - ELETTRONICO. - 343:(2012), pp. 012128-012148. (Intervento presentato al convegno 7th International Symposium on Quantum theory and symmetries (QTS-7) tenutosi a Praga nel 07-13 Agosto 2011) [10.1088/1742-6596/343/1/012128].

Local unit invariance, back-reacting tractors and the cosmological constant problem

BONEZZI, ROBERTO;
2012

Abstract

When physics is expressed in a way that is independent of local choices of unit systems, Riemannian geometry is replaced by conformal geometry. Moreover masses become geometric, appearing as Weyl weights of tractors (conformal multiplets of fields necessary to keep local unit invariance manifest). The relationship between these weights and masses is through the scalar curvature. As a consequence mass terms are spacetime dependent for off-shell gravitational backgrounds, but happily constant for physical, Einstein manifolds. Unfortunately this introduces a naturalness problem because the scalar curvature is proportional to the cosmological constant. By writing down tractor stress tensors (multiplets built from the standard stress tensor and its first and second derivatives), we show how back-reaction solves this naturalness problem. We also show that classical back-reaction generates an interesting potential for scalar fields. We speculate that a proper description of how physical systems couple to scale, could improve our understanding of naturalness problems caused by the disparity between the particle physics and observed, cosmological constants. We further give some ideas how an ambient description of tractor calculus could lead to a Ricci-flat/CFT correspondence which generalizes the AdS side of Maldacena's duality to a Ricci-flat space of one higher dimension.
2012
Journal of Physics: Conference Series
012128
012148
Local unit invariance, back-reacting tractors and the cosmological constant problem / Roberto Bonezzi; Olindo Corradini; Andrew Waldron. - ELETTRONICO. - 343:(2012), pp. 012128-012148. (Intervento presentato al convegno 7th International Symposium on Quantum theory and symmetries (QTS-7) tenutosi a Praga nel 07-13 Agosto 2011) [10.1088/1742-6596/343/1/012128].
Roberto Bonezzi; Olindo Corradini; Andrew Waldron
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/399161
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