The ideas of theoretical physicist Rolf Hagedorn, which had a key role in the development of the physics of ultra-relativistic nuclear collisions, were remembered on the 13 November during a symposium with the title "Hagedorn's legacy", which took place at CERN, organized by Jan Rafelski, Urs Wiedemann and Federico Antinori.

Hagedorn came to CERN in the 50's from the Max Plank Institute of Goettingen to perform calculations of particle orbits in accelerators and joined the theory division of the laboratory. In the beginning of the 60's he started working on the production of particles in hadronic interactions, developing the model of statistical hadronisation, published in 1965 - fifty years ago - in the journal Supplemento al Nuovo Cimento with the title *"Statistical thermodynamics of strong interactions at high energies"*. In this article he discusses one of his key ideas: the existence of an upper limit in the temperature of a hadron system. Hagedorn shows that the only consistent form in the mass spectrum of hadronic resonances, for m → ∞, is the exponential one, and that in the presence of an exponential mass spectrum there is a limiting maximum temperature for a system of hadrons. As one approaches the limiting temperature, an increase in the energy of the system results in the production of resonances with higher and higher mass, with little effect on the kinetic energy of the particles. Hagedorn also gives an estimate for this maximum temperature (nowadays called Hagedorn temperature) of T_{H}=158 MeV (equivalent to approximately 2 x 10^{12} K).

Initially T_{H} was considered as a possible absolute upper limit for the temperature. With the advent of QCD, however, Nicola Cabibbo and Giorgio Parisi realised that T_{H} represents an upper limit for a system of hadrons, but can be exceeded in a deconfined plasma of quarks and gluons, and represents indeed the critical temperature of the deconfinement phase transition.

Rolf Hagedorn also contributed to the birth of the experimental ultra-relativistic nuclear collisions programme; in particular with a work published in 1981 together with Jan Rafelski, in which, for the first time, a signature of deconfinement is proposed, which can survive the phase of re-hadronisation at the end of the collision: strangeness enhancement.

The symposium, attended by more than one hundred participants, retraced the fundamental aspects of Hagedorn's scientific legacy through five reports. In "*50 years of Hagedorn temperature*" Jan Rafelski recalled the fundamental contributions of the German theorist on the limiting temperature and on the prediction of strangeness enhancement in interactions between nuclei. In his presentation *"Hagedorn thermodynamics* *defines its own limits**"* Helmut Satz discussed the connection between the Hagedorn model and the percolation transition, in which, in a system initially composed of neutral hadrons, colour-charge conductive regions are developing progressively. In *"The Hagedorn spectrum and the dual resonance model: an old love affair", *Gabriele Veneziano illustrated how the original connections between Hagedorn's model and the theory of hadronic strings persist when string theory is reinterpreted as a theory of quantum gravity: in this context, upper limits, *"à la Hagedorn"*, could exist for the temperature of a black hole and for that of the primordial universe (with important consequences for the theory of inflation).

In "*Hagedorn's vision in the context of recent lattice and HIC data*" Krzysztof Redlich highlighted the agreement between modern lattice QCD and Hagedorn's calculations on thermodynamic quantities. Finally, in *"Life above the Hagedorn temperature: Quark-Gluon Plasma at SPS, RHIC and LHC"* Berndt Müller evoked a series of milestones which marked the progress of the physics of ultra-relativistic nuclear collisions from its dawn to the present day.

The presentations and videos from the symposium can be found at the symposium's website .

*The original article can be found here .*