9 Syracuse : 1949 – 1952

The year 1949 saw the publication of two papers by Peter Bergmann: Non-Linear Field Theories in the Physical Review [1] and, together with Johanna Brunnings, in the Reviews of Modern Physics [2], with the ambitious title Non-Linear Field Theories II: Canonical Equations and Quantization. These papers lay the foundation for the research of the Syracuse group working to quantize Einstein's theory of general relativity. A year later saw the publication by Paul Dirac of two papers in the Cana-dian Journal of Mathematics [3,4] which were based on a series of lectures he gave in Vancouver in August and September of 1948. These papers, while not concerned with general relativity, dealt with the problem of constructing a canonical formalism for a theory with constraints among the momenta and configuration space variables. Later that year, Pirani and Schild published On the Quantization of Einstein's Gravitational Field Equations [5]. This was their construction of the Hamiltonian for general rela-tivity based on the ideas put forward by Dirac. This amazing flurry of work was all independent except for the stimulation by Dirac of Pirani and Schild. Dirac's papers do not mention general relativity. According to Felix Pirani [6], he and Alfred Schild attended theVancouver lectures. Alfred immediately saw the connection with general relativity and suggested that Felix work with him on the problem for his doctoral dis-sertation. Although the work in Syracuse began without knowledge of the Dirac lectures or that Pirani and Schild existed, I feel that it is important for me to comment and to compare the different basic ideas which led to different constructions of the Hamil-tonian. Dirac's first work in general relativity was published in 1958 [7,8]. It is very closely related to ideas in the Vancouver lectures, but very different from the other constructions. I will take the lecturer's prerogative of including material which is outside my defined limits because the ideas belong inside. Therefore, I shall begin with a comparison of Bergmann and Dirac approaches with emphasis on what theoretical ideas motivated them. Then I will discuss the work at Syracuse in the time frame of my title.