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HEISENBERG'S S-MATRIX PROGRAMME. First edition, extremely rare offprints, of Heisenberg's S-matrix approach to the study of elementary particles. "Heisenberg's prewar researches in quantum field theory, undertaken in part with Pauli, had led him to the study of cosmic rays, the highest energy particles then available for research. When an extremely high-energy cosmic ray strikes the earth's atmosphere, it induces a shower of newly created particles and photons. This effect was to be explained on the basis of quantum field theory. Heisenberg's researches had previously convinced him and others of the inadequacy of field theories for this task. Infinities and divergences plagued all three of the available theories - quantum electrodynamics, Fermi's theory of beta decay (relating to what is now the weak force), and Yukawa's meson theory (relating to what is now the strong, or nuclear, force). The small size of elementary particles and the close approach of the particles to each other in a cosmic ray collision - which triggered the particle shower - indicated to Heisenberg during the 1930s that the difficulties in quantum field theory could be resolved only if a universal minimum length, a new fundamental constant, were introduced into the theory. according to Heisenberg, quantum mechanics itself broke down when applied to events occurring within regions smaller than the size of an elementary particle . Pauli had already suggested that Heisenberg, as he did when formulating the 1925 breakthrough in quantum mechanics, should focus only on observable quantities and attempt to exclude all unobservable variables from the theory. Heisenberg now attempted to do so, at the height of the World War. His effort led to what became after the war his widely studied new theory of elementary particles, the so-called S-matrix theory. In his new approach, Heisenberg used this hypothetical fundamental length to define the allowed changes in the momentum and energy of two colliding high-speed elementary particles. This limitation would help identify the properties of the collision that were observable in present theories. Those at smaller distances were unobservable. For two colliding particles, this yielded four sets of observable quantities with which to work: two of these were the properties of the two particles as seen in the laboratory long before they collide with each other; and two were their properties long after the collision. During the collision they approach within a distance of less than the fundamental length and are thus unobservable. These four sets of observable properties could be arranged in a table, or in this type of work, a matrix, which Heisenberg called the scattering or S-matrix. Although Heisenberg could not actually specify the four elements of the S-matrix, he demonstrated that it must contain in principle all of the information about the collision. In his second paper, completed in October 1942, Heisenberg further showed that the S-matrix for several simple examples of scattering of particles yielded the observed probabilities for scattering. It also gave the possibility for his favorite phenomenon - the appearance of cosmic-ray explosion showers" (Beyond Uncertainty, pp. 347-9). "In a series of papers during the period 1943-1946 Heisenberg proposed as an alternative to quantum field theory a program whose central entity was a matrix he denoted by S and termed the 'characteristic matrix' of the scattering problem . Heisenberg wanted to avoid any reference to a Hamiltonian or to an equation of motion and base his theory only on observable quantities. This emphasis on observables was a return to an idea which had proven useful in his earlier successful formulation of matrix mechanics. Heisenberg's stated purpose in his seminal paper [I.], 'The 'Observable Quantities' in the Theory of Elementary Particles', was to abstract as many general, model-independent features of S as possible. In the abstract and introduction to tha. Seller Inventory # 5971
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