Abstract.
We present a full treatment of the microcanonical ensemble of the ideal hadron-resonance gas starting from a quantum-mechanical formulation which is appropriate for the statistical model of hadronization. By using a suitable transition operator for hadronization we are able to recover the results of the statistical theory, particularly the expressions of the rates of different channels. Explicit formulae are obtained for the phase space volume or density of states of the ideal relativistic gas in quantum statistics as a cluster decomposition, generalizing previous ones in the literature. The problem of the computation of averages in the hadron gas microcanonical ensemble and the comparison with canonical ones will be the main subject of a forthcoming second paper.
Similar content being viewed by others
References
F. Becattini, Z. Phys. C 69, 485 (1996); F. Becattini, Proceedings of XXXIII Eloisatron Workshop on Universality Features in Multihadron Production and the leading effect (1996) 74, hep-ph 9701275; F. Becattini, U. Heinz, Z. Phys. C 76, 269 (1997)
U. Heinz, Nucl. Phys. A 661, 140 (1999); R. Stock, Phys. Lett. B 456, 277 (1999); J. Hormuzdiar et al. , McGill preprint MCGILL-00-04, OITS-686, nucl-th/0001044; H. Satz, Nucl. Phys. Proc. Suppl. 94, 204 (2001); V. Koch, Proceedings of Quark Matter 2002, Nantes, France, 18-24 July 2002, nucl-th/0210070
F. Becattini, U. Heinz, Z. Phys. C 76, 269 (1997); U. Heinz, Nucl. Phys. A 661, 140 (1999); R. Stock, Phys. Lett. B 456, 277 (1999)
R. Stock, hep-ph/0212287
K. Werner, J. Aichelin, Phys. Rev. C 52, 1584 (1995)
F.M. Liu, K. Werner, J. Aichelin, Phys. Rev. C 68, 024905 (2003)
F. Becattini, G. Passaleva, Eur. Phys. J. C 23, 551 (2002)
E. Fermi, Progr. Th. Phys. 5, 570 (1950)
R. Hagedorn, N. Cim. 15, 434 (1960)
F. Cerulus, N. Cim. 22, 958 (1961)
M. Chaichian, R. Hagedorn, M. Hayashi, Nucl. Phys. B 92, 445 (1975)
F. Becattini, L. Ferroni, Statistical hadronization and hadronic microcanonical ensemble II, in preparation
A. Chodos et al. , Phys. Rev. D 9, 3471 (1974)
G. Marchesini, B.R. Webber et al. , Comp. Phys. Comm. 67, 465 (1992).
R. Hagedorn, CERN lectures Thermodynamics of strong interactions (1970); R. Hagedorn, CERN-TH 7190/94, in Hot Hadronic Matter (1994) 13
W. Blumel, P. Koch, U. Heinz, Z. Phys. C 63, 637 (1994)
H. Weyl, The theory of groups and quantum mechanics
D.H. Gross, Eur. Phys. J. B 15, 115 (2000) and references therein
J.V. Lepore, R.N. Stuart, Phys. Rev. 94, 1724 (1954)
R. Milburn, Rev. Mod. Phys. 27, 1 (1955) and references therein; S. Belenkij et al. , Usp. Fiz. Nauk. 62, 1 (1957) and references therein; G. Fialho, Phys. Rev. 105, 328 (1957)
F. Cerulus, R. Hagedorn, Suppl. N. Cim. IX, serie X, 2, 646 (1958)
W.K. Tung, Group theory in physics (World Scientific, Singapore); W. Ruhl, The Lorentz group and harmonic analysis (A. Benjamin, New York 1970)
Author information
Authors and Affiliations
Additional information
Received: 8 July 2003, Revised: 17 October 2003, Published online: 5 May 2004
Rights and permissions
About this article
Cite this article
Becattini, F., Ferroni, L. Statistical hadronization and hadronic microcanonical ensemble I. Eur. Phys. J. C 35, 243–258 (2004). https://doi.org/10.1140/epjc/s2004-01850-1
Issue Date:
DOI: https://doi.org/10.1140/epjc/s2004-01850-1