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Many of the fundamental theories of modern physics can be considered as descriptions of dynamical systems subjected to constraints. The study of these constrained dynamical systems, in particular the problems encountered in formulating them as quantum systems, has many profound links with geometry. These links were explored in the Symposium on Geometry and Gravity, held at the Newton Institute in 1994. This book arose from a conference held during that symposium, and is a collection of papers devoted to problems such as Chern–Simons theory, sigma-models, gauge invariance and loop quantization, general relativity and the notion of time and quantum gravity. They present a lively, varied and topical perspective on this important branch of theoretical physics, from some of the leading authorities in the subject.
In the hills above Florence lies Arcetri, where Galileo Galilei spent his years of house arrest after his trial in 1633. Galileo's statement of the law of inertia launched the study of dynamics on the voyage of discovery and invention on which most if not all of modern physics depends. We also remember Galileo when we speak of Galilean relativity, and it was therefore fitting that it was in Arcetri that the workshop on ‘Constraint's theory and relativistic dynamics’ was held in 1986. This workshop was organised by Giorgio Longhi, Luca Lusanna and Giuseppe Marmo “to examine the current situation of relativistic dynamics”, and I had the good fortune to be able to attend, meeting there many of those who were later to become the “Constraints Club”.
A few years later there arose an opportunity to establish this more formally as an association of researchers active in the area of constrained dynamical systems. Under the European Communities' science programme funds were available for “networks”, and an application was duly prepared to support young postdoctoral fellows to work within the “Constraints Club”, which at that time was a rather loosely coordinated group of five laboratories. This application was unsuccessful, but in 1992 an enlarged (and improved!) application was submitted to the Human Capital and Mobility programme, the successor to science. It too failed, but on resubmission in 1993 was at last accepted, and the network in “Constrained Dynamical Systems” came officially into being on 1 January 1994.