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Societies and Academies

Nature volume 135, pages 198199 (02 February 1935) | Download Citation

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LONDON Royal Society, January 24.—M. BORN and L. INFELD: On the quantisation of the new field equations. (1) The new field theory uses the primary field vectors E, B and derives secondary field vectors D, H by differentiating the Lagrangian L (E, B) with respect to E, B. If one gives up the invariant form (that is, the four-dimensional tensor notation), one can introduce other pairs of primary variables; in each case there exists an action function, one of which is the energy density. Using this representation it is possible to formulate the quantum laws of the field. The field equations can be written without any space or time derivatives, only by means of commutators connecting the field vectors with the total energy and the total momentum. They formulate a coherent Unitarian quantum theory of matter and field. (2) The commutation rules for the field components are given in a new form which makes no use of 8-functions. The behaviour of an electro-dynamical system as a whole is described by a set of integral quantities: total energy, total momentum, centre of energy, total angular momentum. These quantities satisfy commutation, rules which can be derived from those for the field components. The chief result is that the co-ordinates of the centre and the components of the total momentum are connected by the same commutation laws as in quantum mechanics, and that the components of the momentum commute; but the co-ordinates of the centre do not commute. H. BETHE and R. PEIERLS: The scattering of neutrons by protons. The result is practically independent of the special law of force assumed between neutron and proton; it depends only upon the known binding energy of the diplon. The cross-section obtained is about 50 per cent larger than the rather uncertain experimental value. The scattering is almost isotropic (in the relative coordinate system) for neutron energies up to about 40 million volts.

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https://doi.org/10.1038/135198a0

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