The Legacy of Léon Van Hove

The following sections are included:

• CONTENTS

• PREFACE

• INTRODUCTION

Léon Van Hove's research activity in mathematics starts in Belgium in 1945-46 under the supervision of Professor Th. Lepage. Its main content is the variational calculus of multiple integrals of many unknown functions.

After two papers on the construction of the fields associated with some variational problems,^1,2 Léon Van Hove focuses his attention on the extension of the Legendre condition to multiple integrals of many unknown functions: the aim is to show that a minimum condition (formulated by Hadamard) of known necessary character is also sufficient. The solution of the problem is discussed in paper ³ and is the bulk of Léon Van Hove's doctoral thesis (see paper ⁴). In 1949-50 his scientific interests are attracted by the study of the properties of some unitary representations of a group strongly connected to the group of canonical transformations. This group can be considered as characteristic of classical mechanics in its Hamiltonian formulation. In this framework it is important to understand the relation between the unitary representations of the mentioned group and the formalism of quantum mechanics. Preliminary results of this work are presented in two short papers.^5'6 The full discussion on the subject is given in the thesis "d'aggrègation de l'enseignement supérieur" of Léon Van Hove,⁷ which should be considered an important piece of work of great interest also for current research in the field. Referee reports on this paper are reprinted at the end of this note. In 1951 Léon Van Hove approaches some difficult problems on the topological properties of infinitely dimensional Lie groups and in particular on the topological structure of the group of analytical transformations. Following H. Cartan's work he deepens the knowledge on the topological structure of analytical functional spaces. Promising results of this original search are contained in papers ⁸ and ⁹. From 1952 Léon Van Hove's interests in theoretical physics -initiated since 1948- become dominant. A fascinating new chapter of his scientific life now starts, dedicated to problems in nuclear physics, quantum field theory and statistical mechanics. References

During the period 1949-1954, for the most part Van Hove was based at the Institute for Advanced Study, Princeton.¹ He held a standard visiting membership for two terms, 1949-1950 and 1952-1954, and in between his permanent address was the Université Libre, Bruxelles, Belgium. (Nowadays such visiting members of the Institute are called postdocs.) Particle physics was the main programme of work at the time, and it involved R. Oppenheimer and most of the visiting members. By contrast, statistical mechanics and condensed-matter research amounted to a small programme of somewhat unfashionable work, in which G. Placzek had a big hand. Placzek was a permanent member of the Institute from 1948 to 1955. While it was primarily the presence of Placzek that attracted Van Hove to the Institute, he also had E. Wigner at Princeton University, and C. Herring at the Institute for the year 1952-1953.

Since Placzek played a part in Van Hove's work during 1951-1954 it is fitting to recall some of Placzek's activities. First we mention two topics in the scattering of electromagnetic radiation by atoms and molecules. In the period 1931-1933 Placzek developed a quantum theory of scattering by freely oriented molecules which today bears his name. Together with L. D. Landau he revisited A. Einstein's (1910) discussion of Rayleigh scattering by a fluid. The Landau-Placzek formula (1933) gives the ratio of the contributions from entropy and pressure fluctuations to the angular distribution in the undisplaced line in the spectrum of Rayleigh scattering. Critical opalescence arises because the ratio increases without limit as the critical point of the fluid is approached. Moving on in this sketch of Placzek's activities, next we mention work on the scattering of neutrons. The so-called Placzek corrections (1952) to the spectrum account for inelasticity in scattering events that contribute to the structure factor, from which one learns about the spatial distribution of atoms and molecules. As the energy of the primary neutrons increases the corrections become less of a nuisance, and they are unimportant in corresponding experiments performed with X-rays…

In 1955/56 Léon Van Hove published two fundamental papers on perturbation theory of large Quantum systems.^1,2 In these papers he considered features of perturbation theory that are typical for systems with a very large number of degrees of freedom. Examples of such systems are quantum fields, gases , liquids, crystals.

In those days Van Hove was one among the few people who realized that in many essential aspects the quantum theory as developed by Schrodinger, Heisenberg and Dirac leads to serious difficulties when applied to "large" systems. Already three years earlier³ he had pointed out that the ground state and excited states of such a system with and without interaction are mutually orthogonal. In other words, the Hilbert space spanned by the states of the free system does not contain any state of the interacting system. One of the consequences is the formal inapplicability of the Raleigh-Schrödinger perturbation method, as this method is based on the assumption that states of the interacting system can be written as linear combinations of states of the free system.

In his two papers on persistent perturbation effects in continuous spectra Van Hove analyzes the scattering process of particles, where the interaction is considered to be a small perturbation. In the case where the interaction is due to an inter-particle potential, the interaction has a transient effect; only during the time that the particles are close together they will be subject to mutual forces. After a while they will fly away and behave as free particles. In quantum field theory, however, there are the so-called persistent effects…

Once upon a time, shortly after the second World War, when theoretical physicists did not yet write proposals and when they still believed that the vacuum was a heaven of rest, instead of the violently boiling pot of quarks, anti-quarks and gluons, which it now seems to be, there was a young man by the name of T. D. Lee.

He was interested in getting a better understanding of the so called renormalisation of mass and charge, which is a very ingenious and effective method for sweeping a number of difficulties of quantum field theories under the rug.

For a simple model¹ he showed in detail how this method worked.In his model he took a particle, which was fixed in space and which had two internal states, called V and N. The transition between these states was mediated by a meson, which he called θ. The reaction was described by V⇌ N + θ and by a bare coupling constant g⁰.

Lee then showed in detail how all divergences could be incorporated in a redefinition of the V-mass and of the coupling constant. This work was later extended to θ - V scattering and to other sectors.^2,3

However, in spite of the success of the Lee-model, there was a nagging problem. In the limit of an infinite cut-off the renormalised coupling constant went to zero, so that a rather trivial theory remained, giving no scattering at all. In order to obtain a non-vanishing renormalised coupling constant, the bare coupling constant had to be given an imaginary value, giving rise to a so called ghost state with negative norm. Källén and Pauli⁴ showed that this problem could be circumvented by introducing an indefinite metric, but only at paying a certain price: the S-matrix would become non unitary. Since this price is too high, even nowadays, the Lee-model could not be seen as a simple example of a consistent quantum field theory…

At the beginning of the 20-th century, J.W. Gibbs, by a stroke of genius , introduced the concept of statistical ensemble for the description of a many-body system in thermal equilibrium. From here on , equilibrium statistical mechanics could be constructed in a practically deductive way. In particular , the canonical ensemble played a central role. Associated with it is the partition function , a multiple integral over all phase space coordinates of the particles , depending on three parameters , identified with the temperature T, the volume V of the system and the number of particles , N. The partition function is shown to be related to the thermodynamic free energy F(T, V, N) by the simple relation:

F(T,V,N) = -k_BTlnZ(T,V,N)

where kB is the Boltzmann constant…

Léon Van Hove is a pioneer of the modern theory of irreversible processes based on the spectral representation associated to dynamical systems.

Non-equilibrium physics deals with one of the most fundamental problems: the microscopic description of irreversibility. It is no doubt that irreversibility is an essential ingredient of nature. As the fundamental laws of physics are time-symmetric (Newton's law, quantum mechanics), physicists have struggled to comprehend the relation between irreversibility and the fundamental laws for more than a century. A still popular approach is that irreversibility appears as the result of our approximations, such as coarse- graining. However, specially after the discovery of the constructive role of irreversibility (as shown by the appearance of dissipative structures, far from equilibrium) it is difficult to accept this naive argument. Another popular view is that irreversibility is a result of special initial conditions of our universe. This is also difficult to accept, because we see at present both reversible processes studied in classical dynamics and irreversible processes. One may state that it is only recently we did start to understand the mechanism of the appearance of irreversibility.

Modern theory of irreversibility owes to Van Hove three important contributions, the Van Hove limit (the so-called λ²t limit), the discovery of delta function singularities, and the generalized master equation…

Please refer to full text.

Scattering has been a dominant theme in the scientific work of Léon Van Hove. Starting with his influential work on neutron scattering during his Princeton years in the early fifties, it continued at CERN from about 1960 onwards with high energy scattering of hadrons, i.e. of quarks . In the last decade of his life he was the stimulating nucleus of an activity on multiparticle production and dynamics.

Very soon after the advent of nuclear reactors , i.e. very soon after the Second World War, it was realized that the beams of thermal and slow neutrons coming from a reactor, could be fruitfully used for the investigation of condensed matter systems . In fact , the use of slow neutrons has certain advantages with respect to the use of X-rays, which makes neutron scattering especially important for the study of dynamical properties of condensed many-particle systems, like solids , liquids and dense gases . The important point is that both the momentum and the kinetic energy of the neutrons are ideally matched to the equivalent quantities characteristic of atomic excitations and fluctuations in condensed matter , whereas for photons , whether as light or as X-rays , this happy coincidence never occurs . Moreover, the fact that neutrons possess a magnetic moment enables the study of magnetic structure. Neutron scattering has become one of the main tools for investigating the dynamic structure of condensed matter systems , in the case of liquids it is still the main tool . Van Hove 's work in the mid-fifties on the relation between inelastic neutron scattering and crystal dynamics and his elegant and general formulation of the theory of neutron scattering by an arbitrary system of interacting particles in terms of space-time correlation functions , or pair distribution functions , G(r, t) and G_s (r, t), can rightly be regarded as forming the cornerstone of part and present-day thinking on the interpretation of neutron scattering experiments. The impact of his neutron scattering papers (expressed by the number of citations) has been extraordinarily high, unsurpassed I think by any of his other papers . Their direct , practical use to the experimenter is quite remarkable for a theoretical physicist who started his career as a pure mathematician. This chose connection to and interest in experimental work he also showed during his CERN-period…

Several periods in the scientific career of Léon Van Hove demonstrate how progress in a very complex field can be reached by means of "a very close interplay between phenomenological analysis of sufficiently accurate experiments, . , and application of the few general theoretical principles .". One of these periods is ranging from Longitudinal Phase Space to Analytical Multichannel Analysis. The experimental applications are historical by necessity, but the basic ideas also apply to future experiments.

In this series of papers^1,2,3 Léon Van Hove, in collaboration with Stefan Pokorski, attacked the problem of multiparticle production in what is now called `soft' hadronic collisions.

Their starting point was the idea of independent production of hadronic clusters. It emerged somewhat earlier from the studies of two-particle correlations which turned out to be of short range and consistent with those expected from isotropic decay of clusters with average number of about 2 charged particles.

Van Hove and Pokorski associated this phenomenon with the fresh discovery of `glue', the strongly interacting`stuff' carrying about 1/2 of the hadron momentum. Their model¹ is very simple: In a high-energy collision the glue is responsible for interaction, whereas the quarks (the current quarks in to-days' s language) pass undisturbed. The glue is `shaken off' in a sort of (strong) bremsstrahlung process, thus producing independent gluonic clusters in the central region of rapidity. The unperturbed current quarks dress themselves again and form two`leading' clusters.

This simple picture, accompanied by the relation between the leading particle energy loss and density of particles in the central region derived some time before by Stodolsky,⁴ turned out to describe very well the particle spectra in central and in fragmentation regions as well as the overlap function, a notorious problem for most of the models of multiparticle production…

The paper ¹ considers passage of a strongly interacting system through nuclear matter. At the time the paper was written, this problem became very acute: the accumulating experimental evidence on particle production from nuclear targets seemed to be in blatant contradiction with the Glauber theory of these phenomena. Van Hove explained the observed effects and showed how to apply correctly the Glauber theory to high-energy scattering of strongly interacting objects.

The experiments² measured the cross-section for production of three and five pions whose energy was close to that of the incident pion beam. The naive application of the Glauber theory was to assume that the incident pion fluctuates into the three (five) pion system observed in the final state which then passes through the nuclear matter. The observed cross-section is then the product of the fluctuation probability and of the probability that the fluctuation did not suffer any substantial energy loss in nuclear matter. When the data were analysed this way, a surprising result came out: the obtained cross-section for inelastic interaction of the three-pion system was about equal to that of pion, and the cross-section for five-pion system was even smaller. This clearly contradicted a common sense and also did not agree with any theoretical estimates available at the time.

Van Hove realized that the problem lies in the multichannel character of the process. Since the system passing through the nucleus is strongly interacting, its successive scatterings can easily transform it into another state. Thus the system entering the nucleus is, in general, rather different from the one observed in the final state. Consequently, we have to consider a multichannel problem. Moreover, the number of channels is so large and they are so dense (as the system is strongly interacting) that one may approximate these transitions by a continuous scattering matrix. It is then natural to study eigenstates of this matrix for which the standard Glauber theory does apply (by definition they do not change when interacting in the nucleus). Since the corresponding eigenvalues differ from each other, various eigenstates are differently absorbed in the nucleus and thus the system is strongly modified.

This idea of decoupling of the system observed in the final state from that which enters the nucleus, and the use of the eigenstates of the continuous scattering matrix rather than the matrix itself, became common tools in the description of these phenomena and represent now the standard method of calculation. Today the eigenstates of the scattering matrix are usually modelled by a multi-quark system at fixed (transverse) position of its components³ but the basic idea remains the same as suggested by Leon Van Hove about 30 years ago.

Léon Van Hove played a very important role in the genesis and early development of the heavy ion programmes, which started at CERN and at Brookhaven in the mid eighties. By the early eighties it had been realized that heavy ion collisions at high energy could give conditions suitable for the formation of a quark-gluon plasma. Whereas under normal conditions quarks are confined within colour neutral hadrons, it is expected that at high enough temperature and/or high enough density, they should be deconfined into a quarkgluon plasma. The needed baryon density at low temperature is an order of magnitude above that of nuclear matter (0.15 GeV/fm³). The needed temperature, at low baryon density, is of the order of 150 to 200 MeV. The latter condition prevailed in the early Universe which should have been a quark-gluon plasma until 10 microseconds after the Big Bang. The former one is likely to prevail in the core of neutron stars.

In a head-on heavy ion collision at very high energy, a blob of quark gluon plasma could be formed over a volume covering the colliding ions . It would quickly blow itself apart into a hadron gas as it expands and cools down. There could however be enough specific features in the final state secondary distribution to signal the formation of the plasma and provide information about the phase transition…

Multiparticle dynamics was for Léon a meeting ground between particle and statistical physics, the natural field for a fruitful dialog between theory and experiment. Open problems in multiparticle dynamics represented to him a stimulating domain of investigation: here he could use all his extraordinary knowledge in theoretical and statistical physics, which led him to important results since the beginning of his career, together with a continuous confrontation with experimental facts, which CERN atmosphere allowed and requested.

Papers^1,2,3,4,5 reprinted at the end of this Section contain a selection of his most relevant contributions in the field in the eighties. They move from the interpretation of the observation of UA5 Collaboration at the CERN pp collider on NB regularity in charged particle multiplicity distributions to the claim that QCD parton showers formation with generalized (or strong) local hadron parton duality is the dynamical mechanism responsible of multiparticle production in e⁺e^- annihilation, lepton-hadron, hadron-hadron and ultrarelativistic heavy ion collisions [see also Section 1.3.4]. Paper ⁶ is the last contribution written by Leon and it can be considered a summary of the main results of what had to be the first part of a joint programme of collaboration initiated in Amalfi since 1984. As Leon used to repeat, "It should be stressed that NB regularity and (generalized) local hadron parton duality are only approximate properties of multiparticle production [.] There is nothing surprising in this situation. It is totally excluded that NB distribution with its two parameters could describe accurately all the complexities of particle production, whatever the basic dynamical mechanism. Although they are only approximate, the NB regularities are important in two ways. They give extremely compact descriptions of many properties in terms of very few parameters, and they have been shown to be good revealers helping to guess among many possibilities what are the likely dynamical mechanisms, QCD parton showers and our generalization of local parton hadron duality".⁷ The aspect of the regularities which made Leon particularly happy was indeed its interpretation in terms of clans and their related beautiful properties in different classes of collisions. He considered that `a surprise', with a deep physical insight.

I will try to follow the logic which inspired this search…

It is almost eighteen years ago since I first visited Léon Van Hove at CERN in Geneva to discuss the general outline of the first ESO-CERN Symposium. It was a very exciting moment. On the way to his office Léon told me that just a few days before all CERN's staff had gathered in the large auditorium to listen to a seminar in which the discovery of the W and Z particles had been announced. So we sat down in Léons's office full of enthusiasm.

After so many years it is perhaps worth mentioning that the scientific and technical divisions of ESO have been hosted in the CERN campus for many years during which CERN provided not only logistical but also a very much appreciated technical support to ESO deeply engaged in the realization of its first large telescope , the 3.6m, to be located at La Silla in the Chilean Andes. When Léon became Research Director General of CERN in 1976 this positive attitude toward the sister European organization continued, but it so happened that it was just toward the end of his mandate that ESO had to move to the new headquarters in Garching. In the course of a distinguished symposium, held on the occasion of the inauguration ceremonies of ESO headquarters in 1981, Léon gave an inspiring lecture on "Particle Physics in the Early Universes"¹ which in a way established an ideal link between the two European organizations now being physically separated by hundreds of kilometers…

When in 1954 Léon Van Hove was offered a full-professorship at the University of Utrecht he was just 30 years of age. This chair of Theoretical Physics was vacated in 1953 by S.R. de Groot when he was appointed in Leiden and was previously occupied by H.A. Kramers, G.E. Uhlenbeck and L. Rosenfeld. Van Hove may well have been the youngest professor in the Netherlands at that time.

As was the custom in the Netherlands, at each university institute there was only one professor who was at the same time director. At that time the Institute of Theoretical Physics in Utrecht consisted in addition to the professor of a lector B.R.A. Nijboer, an assistant N.G. van Kampen, four graduates and a secretary, housed in the three-room ground-floor of an old merchant house in the center of the town.

Those who feared that his young age would turn out to be a handicap for his functioning as a professor and director were soon reassured. His amiable personality and his quiet self-confidence and mature behaviour made him look older than he was. He had welldefined opinions and could bring them convincingly . The fact that he came from abroad worked rather to his advantage. He was less impressed by old hierarchical structures than a Dutchman would have been at that age. Furthermore he brought some novel ideas. For example, he broke with the old rule that there is only one professor for each discipline. A year after his arrival in Utrecht Ben Nijboer was appointed full-professor followed a few years later by a similar appointment for Nico van Kampen. Other universities were soon to follow…

Particle accelerators and large experimental apparatus have played a dominant role in the scientific world of the last decades. In particular they have led to the clarification of the composition of matter as founded on elementary constituents and to the verification of the underlying symmetry laws.

It was by far not a simple process, but it went instead via a tortuous route marked by phases of apparent growing complexity, proliferation of particles, puzzling ambiguities and a need for classifying the rich spectrum of hadrons. The development of particle accelerators from the hundred-MeV region to multi-GeV and well beyond went hand in hand with the need to tackle and solve the queries posed by the growing edifice of particle physics.

Léon Van Hove had the good fortune to live through the main arc of this development, which culminated with his involvement in the discovery of the intermediate bosons at CERN.

In 1972, at a kind of half mark point, Léon had published a survey of the field as he had seen it developing during 25 years.1 Some of the questions raised there (e.g. the high mass region of hadron spectra, the possible existence of more leptons, the high energy behaviour of the weak interaction) were in fact going to be answered later.

After completing his mandate as Director-General for research, Léon Van Hove remained at CERN and came back to the Theory Division taking back the staff post which he had left when moving to the Directorate. I was head of the Division from 1982 to 1988, a period covering most of the time which he then spent there before his retirement. I of course found it a little peculiar to be his official `boss', when I had first come to CERN, 15 years before, looking at him as one does toward a great master. But, as well known to his many friends, Leon extended his friendship in a way which left little room for hierarchical matters, one way or the other.

I was really impressed to see how the great physicist whose advice was looked for on many important questions, took his staff member role in the Division very seriously. He participated actively in the Staff meetings with homework done. For Léon there were no big or small jobs. There were only the jobs to be done and which had to be done seriously.

At that time he took important advisory responsibilities within ESA where, in particular, he chaired the Science Programme Committee (SPC). This is a very important committee where the scientific projects have to be approved and funded by representatives from the Member States. This is reported elsewhere. He also continued actively his research work, with particular attention to heavy ion collisions and to multiplicity distributions, often working with younger colleagues. This is also reported elsewhere…

Léon Van Hove joined CERN in the year 1961 as leader of the CERN theory division - and this was the beginning of a fruitful interaction between an eminent theorist and the experimental physicists working at the CERN accelerators, which lasted more than 20 years. In that time Léon had a strong impact on the scientific program of the laboratory through both, his scientific discussion with the experimentalists, and his function as a member of the program committees, member of the CERN directorate, and most prominently of course as Director General responsible for the research program in the laboratory in the years 1976-1980.

In his first years at CERN, his scientific interest and his close contacts with experimentalists concentrated on the physics of hadrons, the physics of the strong interaction, especially questions of multiparticle dynamics. This was the field of his own scientific activity at that time, where he had made several important contributions. This field remained his love until the end of his life. He later widened his scientific interest and as Director General he mastered with his clear insight the scientific aspects of the full range of the CERN research program and was an interested and competent discussion partner for the physicists working at CERN.

The nomination as CERN Director General, jointly with John Adams, for the years 1976-1980 by the CERN Council was a turning point in Léon's life. As "Director General-research", he had to give up almost completely his own research in theoretical physics and take the responsibility for the ongoing experimental program and for the future direction.

The five years of his term were a very fruitful period for CERN, marked by the start-up of the SPS with its excellent research facilities, by important decisions for broadening the SPS program including the decision for the antiproton program, and by the planning for LEP…

The proton-antiproton (pp) collider story began at CERN with C. Rubbia's proposal to implement on the CERN accelerators an idea originally due to G. I. Budker (Novosibirsk, USSR). Rubbia's proposal was simultaneously addressed to the Fermi National Accelerator Laboratory (Fermilab) in Batavia (USA), but this is one instance where the Europeans acted faster than their American colleagues. The CERN pp project, approved in 1978 after completion of the necessary tests, was carried out in a record time of three years. Experiments could begin in 1981, and early in 1983 two teams of scientists achieved the major discovery which formed the principal justification of the enterprise; they established the existence of the W and Z particles, the carriers of the weak interactions, with the properties predicted by theorists some fifteen years earlier. These experiments are absolutely crucial for our understanding of the basic forces of nature.

It so happened that for the five year period 1976-80 I was responsible for the research activities of CERN. I was therefore closely involved in the definition of the project, and much of the burden rested upon me when the time came for CERN to select it among several proposals and launch its realization. What follows is a personal account of this interesting phase in the recent history of CERN and of European physics…

From October 1971 to September 1974 Léon Van Hove was for three years a Scientific Member, the chairman of the directorate and the Managing Director of the physics institute within the Max-Planck-Institut fur Physik and Astrophysik in Munich . This article gives an overview of his main activities and achievements in the institute during this fruitful and successful period.

Nearly ten years after he passed away, Léon Van Hove is very clearly present in my memory and when I recall his enthusiasm and openness to every area of science, I regret even more that he cannot share with us the success of ESA's science missions. Indeed, Léon Van Hove played a key role in ESA 's Space Science Programme. In 1983, following the suggestion of G. Setti, he was invited to join the Survey Committee, chaired by J. Bleeker, whose task was to formulate ESA's Long-Term Space Science Plan, which in 1984 was christened the Horizon 2000 Programme. The idea was to incorporate in the Committee physicists who could strengthen the relationship between the space physics and particle physics communities. Our choice could not have been better. Léon Van Hove played his role magnificently and, in spite of the different and very often new character of this field of science for him, participated fully in the discussions and in the elaboration of the Programme.

We benefited on many occasions from his profound scientific knowledge, his remarkable critical judgement and his ability to assess rapidly the quality of any new idea and any new project. He helped on many occasions in the making of final and often difficult decisions. When the Survey Committee held its last meeting in May /June 1984 in Venice, it was Léon Van Hove who suggested after the first three cornerstones of the programme had been agreed, i.e. the X-ray and submillimetric observatories and the mission to return pristine material from asteroids or comets, now better known as XMM, FIRST and Rosetta respectively, that a fourth cornerstone be created incorporating both the Cluster and SOHO projects together in a unique Solar-Terrestrial Programme…

Who was Léon Van Hove? It is easy to answer summarily : a great scientist entirely devoted to science. But this does not do justice to the many facets of his character and opinions, which this section will try to describe with specific examples.

We will as much as possible use Léon's own words from his speeches and letters, extracted from his own notes (we have translated some of these from the French ). It may be of interest in this context to also consult Léon's short autobiography, which he wrote toward the end of his life, and which opens this volume.

The following sections are included:

• Curriculum vitae, Awards and Memberships

• Publication List