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Is there more than one “Curie’s principle”? How far are different formulations legitimate? What are the aspects that make it so scientifically fruitful? This article is devoted to exploring these questions. We begin by discussing Curie’s original 1894 article. Then, we consider the way that the discussion of the principle took shape from early commentators to its modern form. We say why we think that the modern focus on the interstate version of the principle loses sight of some of the most significant applications of the principle. Finally, we address criticisms of the principle put forward by John Norton and Bryan Roberts.
The period between the years 1976 and 1984 shows very little activity in string theory. As we mentioned in the previous Part, a lot of work went into developing both perturbative and nonperturbative aspects of QCD, which established itself as the theory of strong interactions. Lattice gauge theory was formulated and the idea of confinement was developed. These were also the years when supersymmetry was used to construct the Minimal Supersymmetric Standard Model, and the various supergravities were obtained. The most fundamental of them, constructed by Cremmer, Julia and Scherk, was the eleven-dimensional one. The fact that the various supergravities showed better ultraviolet behaviour than the original gravity theory gave the hope that one could unify gauge interactions with gravity in the framework of supergravity without nonrenormalizable divergences. On the other hand, the machinery of string theory seemed too complicated and unnecessary for unification. We review these developments in Section 42.2.
Although research in string theory was very limited in these years, it led to three fundamental developments. The first one, discussed in the Chapter by Green, was the reformulation of the fermionic string in terms of a light-cone fermionic coordinate Sa, that is an SO(8) spinor, instead of the light-cone SO(8) vector ψi of the RNS model. This allowed the complete construction of type IIA, IIB and I superstring theories. It is described in Section 42.3.
The construction, from the axioms of S-matrix theory, of the Veneziano model and of its extension to N external particles, the Dual Resonance Model, made many people believe that this theory was completely different from quantum field theory. However, it soon became clear that the DRM was actually an extension of, rather than an alternative to, the various field theories, such as φ3 scalar theory [Sch71], gauge theories [NS72] and general relativity [Yon73, SS74, Yon74].
The DRM contains a parameter, the slope of the Regge trajectory α′ with dimension of (length)2, or its inverse, the string tension T = 1/(2πα′). The study of DRM amplitudes in the zero-slope (or infinite string tension) limit shows that these reduce to Feynman diagrams of specific field theories. In the string picture of the DRM, an intuitive way of understanding the zero-slope limit is the following. The string tension has the tendency to make the string collapse to a point, but, if the string is moving, for example rotating, there is also the centrifugal force, which has the opposite tendency. This means that a possible string motion results from the balance between these two forces. However, in the zero-slope limit the string tension is increasingly large, the centrifugal force cannot balance it anymore, and the string collapses to a point. In this limit, string theory becomes a theory of pointlike objects that is described by ordinary quantum field theory.
Part V deals with the extensions of the Dual Resonance Model (DRM), i.e. the bosonic string, to include additional symmetries and degrees of freedom. These generalizations were originally motivated by the need to overcome the drawbacks of the DRM and obtain a more realistic model of hadrons. Such attempts were only partially successful, though, with hindsight, we can say that they added some essential elements for the construction of modern string theory.
One of the first modifications of the Koba–Nielsen amplitude aimed at incorporating the internal flavour symmetry of hadrons, and was proposed by Chan and Paton in 1969. As discussed in Section 27.2, these authors showed that an internal flavour symmetry can be introduced simply by multiplying the amplitudes by appropriate group theoretical factors. Such factors can be viewed as resulting from the presence of a quark–antiquark pair attached to the open string end-points, and carrying flavour quantum numbers.
However, the incorporation of flavour symmetry was not the only open issue. As discussed in the previous Parts, the main problems of the DRM were: (i) the presence of a tachyon; (ii) the absence of fermions, preventing the description of baryons; (iii) the presence of a critical dimension with an unrealistic value, d = 26. Attempts to solve these problems started very early, in fact immediately after the appearance of the Veneziano formula, and went on more or less in parallel with the understanding of the DRM and its reinterpretation as a quantum string (see Parts III and IV).
String theory describes one-dimensional systems, like thin rubber bands, that move in spacetime in accordance with special relativity. These objects supersede pointlike particles as the elementary entities supporting microscopic phenomena and fundamental forces at high energy.
This simple idea has originated a wealth of other concepts and techniques, concerning symmetries, geometry, spacetimes and matter, that still continue to astonish and puzzle the experts in the field. The question ‘What is string theory?’ is still open today: indeed, the developments in the last fifteen years have shown that the theory also describes higher-dimensional extended objects like membranes, and, in some limits, it is equivalent to quantum field theories of point particles.
Another question which is also much debated outside the circle of experts is: ‘What is string theory good for?’ In its original formulation, the theory could not completely describe strong nuclear interactions; later, it was reproposed as a unified theory of all fundamental interactions including gravity, but it still needs experimental confirmation.
This book will not address these kinds of questions directly: its aim is to document what the theory was in the beginning, about forty years ago, and follow the threads connecting its development from 1968 to 1984. Over this period of time, the theory grew from a set of phenomenological rules into a consistent quantum mechanical theory, while the concepts, physical pictures and goals evolved and changed considerably.
By 1973 two ghost-free dual models had been constructed, the Dual Resonance Model and the Ramond–Neveu–Schwarz model. The structure underlying the DRM was that of a relativistic string described by the Nambu–Goto action, but it was not clear yet which kind of string was underlying the RNS model. These models were not suitable for describing strong interactions because they both had massless particles with spins one and two in their spectra (together with a tachyon). An additional problem was raised by the deep inelastic experiments: probing the structure of protons at short distances, they showed the existence of pointlike particles that could be interpreted as the quarks. As already mentioned, string theory scattering amplitudes were too soft at large momentum transfer to explain these experiments. Therefore many researchers went back to field theory; in particular, quantum chromodynamics (QCD), the non-Abelian gauge theory for quarks and gluons formulated in 1972, was intensively studied in the following years obtaining convincing experimental support.
Although these events implied that dual theories could not correctly describe the hadronic processes, they did not completely put an end to their study. In fact, some of the earlyworkers in this field were so attracted by the consistent and deep structure of these models that they continued to study them, sometimes at the price of putting their careers at risk.
In May 2007 we organized a workshop on the origin and early developments of string theory at the Galileo Galilei Institute for Theoretical Physics in Arcetri (Florence). A fair number of researchers who had contributed to the birth of the theory participated and described, according to their personal recollections, the intriguing way in which the theory developed from hadron phenomenology into an independent field of research. It was the first occasion on which they had all been brought together since the 1975 conference in Durham, which represented the last meeting on string theory as applied to hadronic physics.
The workshop in Arcetri was a success: the atmosphere was enthusiastic and the participants showed genuine pleasure in discussing the lines of thought developed during the years from the late Sixties to the beginning of the Eighties, mutually checking their own reminiscences. This encouraged us to go on with the project we had been thinking of for some time, of an historical account of the early stages of string theory based on the recollections of its main exponents. We were fortunate enough to have on board practically all the physicists who developed the theory. While some of the contributions to this Volume originated from the talks presented at the meeting, most of them have been written expressly for this book.
In starting this project we were motivated by the observation that the history of the beginnings and early phases of string theory is not well accounted for: apart from the original papers, the available literature is rather limited and fragmentary.