RSS feeds
ÐóññêèéEnglish
Issue 4, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2013

 / 

September

←  →

Methodological notes


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.

Fulltext pdf (596 KB)
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)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

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

References (43) Cited by (7) Similar articles (20) ↓

  1. V.A. Aleshkevich “On special relativity teaching using modern experimental data” 55 1214–1231 (2012)
  2. P.B. Ivanov “On relativistic motion of a pair of particles having opposite signs of masses” 55 1232–1238 (2012)
  3. V.P. Makarov, A.A. Rukhadze “Force acting on a substance in an electromagnetic field” 52 937–943 (2009)
  4. A.I. Musienko, L.I. Manevich “Classical mechanical analogs of relativistic effects” 47 797–820 (2004)
  5. V.B. Morozov “On the question of the electromagnetic momentum of a charged body” 54 371–374 (2011)
  6. M.I. Krivoruchenko “Rotation of the swing plane of Foucault’s pendulum and Thomas spin precession: two sides of one coin” 52 821–829 (2009)
  7. V.I. Ritus “Permutation asymmetry of the relativistic velocity addition law and non-Euclidean geometry” 51 709–721 (2008)
  8. V.I. Ritus “On the difference between Wigner’s and Møller’s approaches to the description of Thomas precession” 50 95–101 (2007)
  9. G.B. Malykin “The Sagnac effect: correct and incorrect explanations” 43 1229 (2000)
  10. G.B. Malykin “The relation of Thomas precession to Ishlinskii’s theorem as applied to the rotating image of a relativistically moving body” 42 505–509 (1999)
  11. Yu.I. Hovsepyan “Some notes on the relativistic Doppler effect” 41 941–944 (1998)
  12. A.A. Logunov “The theory of the classical gravitational field” 38 179–193 (1995)
  13. A.A. Logunov, Yu.V. Chugreev “Special theory of relativity and the Sagnac effect” 31 861–864 (1988)
  14. S.I. Syrovatskii “On the problem of the ’retardation’ of the relativistic contraction of moving bodies” 19 273–274 (1976)
  15. G.B. Malykin “Sagnac effect in ring lasers and ring resonators. How does the refraction index of the optical medium influence the sensitivity to rotation?” 57 714–720 (2014)
  16. V.I. Ritus “Lagrange equations of motion of particles and photons in the Schwarzschild field” 58 1118–1123 (2015)
  17. X.-B. Huang “A rigorous minimum-assumption derivation of the Lorentz transformation” 54 529–532 (2011)
  18. G.B. Malykin “Para-Lorentz transformations” 52 263–266 (2009)
  19. K.Yu. Todyshev “Measuring the inclusive cross section of e+e− annihilation into hadrons in the pre-asymptotic energy range” 63 929–939 (2020)
  20. V.I. Ritus “Generalization of the k coefficient method in relativity to an arbitrary angle between the velocity of an observer (source) and the direction of the light ray from (to) a faraway source (observer) at rest” 63 601–610 (2020)

The list is formed automatically.
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions