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.

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) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 7th, February 2013, accepted: 27th, February 2013 Оригинал: Гаите Х «Релятивистская теорема вириала и масштабная инвариантность» УФН 183 973–986 (2013); DOI: 10.3367/UFNr.0183.201309f.0973