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The relativistic virial theorem and scale invariance


Instituto Universitario deMicrogravedad Ignacio DaRiva delaUniversidad Politécnica deMadrid, 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.

Text can be downloaded in Russian. English translation is available here.
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/
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

:   «   » 183 973–986 (2013); DOI: 10.3367/UFNr.0183.201309f.0973

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