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The relativistic virial theorem and scale invariance


Instituto Universitario de Microgravedad ‘Ignacio Da Riva’ de la Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, Madrid, E-28040, Spain

The virial theorem is related to the dilatation properties of bound states, as seen in particular from the relativistic virial theorem formulated (by Landau and Lifshitz) in terms of the energy-momentum tensor trace. In the Hamiltonian formulation of dilatations we propose here, the relativistic virial theorem naturally arises as a stability condition against dilatations. A bound state becomes scale invariant in the ultrarelativistic limit, in which its energy vanishes. However, for very relativistic bound states, scale invariance is broken by quantum effects, necessitating including the energy-momentum tensor trace anomaly into the virial theorem. This quantum field theory virial theorem is directly related to the Callan — Symanzik equations. The virial theorem is applied to QED and then to QCD, focusing on the hadronic bag model. In massless QCD, 3/4 of the hadron mass corresponds to quarks and gluons and 1/4 to the trace anomaly, according to the virial theorem.

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Fulltext is also available at DOI: 10.3367/UFNe.0183.201309f.0973
PACS: 03.30.+p, 11.10.St, 12.38.Aw, 12.39.Ba (all)
DOI: 10.3367/UFNe.0183.201309f.0973
URL: https://ufn.ru/en/articles/2013/9/e/
000328748500005
2-s2.0-84890510622
2013PhyU...56..919G
Citation: Gaite J "The relativistic virial theorem and scale invariance" Phys. Usp. 56 919–931 (2013)
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Received: 7th, February 2013, 27th, February 2013

Îðèãèíàë: Ãàèòå Õ «Ðåëÿòèâèñòñêàÿ òåîðåìà âèðèàëà è ìàñøòàáíàÿ èíâàðèàíòíîñòü» ÓÔÍ 183 973–986 (2013); DOI: 10.3367/UFNr.0183.201309f.0973

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