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We argue that the sole requirement of a self-consistent bootstrap including all hadrons up to infinite mass leads to asymptotically exponential laws for the hadron mass spectrum, for momentum distributions, and for form factors (and to a highest temperature).

The understanding of Hagedorn’s pivotal discovery, the exponential mass spectrum, evolved rapidly. Some of the insights have since been lost from view—I recall the relevance of the preexponential power index . Moving forward to current lattice QCD computation of QGP properties I describe an emerging relationship.

A large number of research papers motivated Rolf Hagedorn to prepare a guide to the Statistical Bootstrap Model literature in mid-1972; he wanted to show the reader a) which publications best prepare the uninitiated, b) how different publications relate to each other, and c) he aimed to connect similar developments into groups. The two figures classify in this fashion the research works, providing in the rendition the relevant Refs. [[]–[]]. The editor updated all preprint citations for the 2015 printing.

We formulate the statistical bootstrap model for nuclear matter, and study its resulting thermodynamic properties at nuclear densities below the saturation density. We discuss the relevance of limiting temperature and the phase transition gas–‘liquid’ when the volume of the fireball grows with its energy.

We employ the technique of the analytically continued grand canonical pressure partition function to show that, under physically meaningful boundary conditions (non-existence of external confining vessels, i.e., no fixed volumes), the energy density and similar intensive quantities do indeed have, in a statistical bootstrap model of extended hadrons (van der Waals type volume corrections), the singularity claimed in previous papers. Earlier results obtained with an entirely different technique (which had been criticized) are recovered and shown to be correct. The technique used here is useful in all cases where the volume is not imposed from the outside but results from the internal dynamics of the system, as is generally the case in high energy physics and astrophysics.

Rolf Hagedorn reminisces in 1984 about limiting temperature, the development of the statistical bootstrap model (SBM). He argues that consideration of hadrons of finite size allowed the generalization of SBM into a sophisticated relativistic van der Waals-type gas, leading on to a theory of phase transformation from melting hadrons to boiling quarks.

A qualitative review is given of the theoretical problems and possibilities arising when one tries to understand what happens in relativistic heavy ion collisions. The striking similarity between these and collisions suggests the use of techniques similar to those used 5–12 years ago in collisions to disentangle collective motions from thermodynamics. A very heuristic and qualitative sketch of statistical bootstrap thermodynamics concludes an idealized picture in which a relativistic heavy ion collision appears as a superposition of moving ‘fireballs’ with equilibrium thermodynamics in the rest frames of these fireballs. The interesting problems arise where this theoretician’s picture deviates from reality: non-equilibrium, more complicated motion (shock waves, turbulence, spin) and the collision history. Only if these problems have been solved or shown to be irrelevant can we safely identify signatures of unusual states of hadronic matter as, for example, a quark-gluon plasma or density isomers.

The theory of hot nuclear fireballs consisting of all possible finite-size hadronic constituents in chemical and thermal equilibrium is presented. As a complement of this hadronic gas phase characterized by maximal temperature and energy density, the quark bag description of the hadronic fireball is considered. Preliminary calculations of temperatures and mean transverse momenta of particles emitted in high multiplicity relativistic nuclear collisions together with some considerations on the observability of quark matter are offered.

In 1980/81 the ISR community of Physicists at CERN was preparing for a heavy ion experimental program. My lecture was moved-up from a later -meeting after another speaker bowed-out from the -meeting. Before describing my presentation, I provide a few circumstantial details of potential interest.

I present the heavy ion program development at CERN, reproducing much of the pivotal discussion at the 123th meeting of the CERN Scientific Policy Committee (SPC), Geneva—21 and 22 June 1982, based on the Draft Minutes of the meeting (CERN/SPC/0490/Draft, 1982) and related clarifications as marked.