Gauge Theories of Massive and Massless Tensor Fields

概要

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Extension of the Poincare group is performed by replacing its ten constant parameters by ten arbitrary functions. (For the purpose of comparison, similar procedures to extend a direct product of translation and internal symmetry groups are also carried out). Two independent sets of gauge fields are introduced corresponding to the group structure of semi-direct product of the translation and Lorentz groups. It is an essentially new result that the gauge fields associated with the Lorentz group can be massive only when free Lagrangians for both sets of gauge fields are considered simultaneously. It is shown that there are two solutions to satisfy the requirement that there should be no mass terms in resultant equations. A choice adopted in this paper is to impose field-field strength identity, viz. to represent the gauge fields of the Lorentz group in terms of the field strengths associated with the translation group; thus we obtain a set of equations to govern gravitation and further symmetrized energy-momentum tensors as its sources. All arbitrary coefficients (except for a cosmological constant) in free Lagragians are determined by means of linear approximation. With a reasonable identification between the gauge fields and the metric tensors, the ensuing equations are shown to be equivalent to Einstein's equation of gravitation.
理論物理学刊行会の論文
1968-02-25