(3+1)-Structure of Space-Time in <Poincare>^^^- Gauge Theory of Gravity : Particles and Fields

概要

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The (3+1)-structure of space-time in a <Poincare>^^^- gauge theory of gravity proposed in a previous work is studied. It is shown that there is a unit, time-like vector field N on the space-time manifold M. This together with an R^4-valued higgs type field ψ, corresponds to a global cross section of an associated bundle of the principal fiber bundle over M having the covering group of the Poincare group as the structure group. The field N is inherent in the formulation and coincides with the 0-th of the vierbein fields in particular gauges. Frobenius's condition for N, which ensures the existence of a slicing of M into a family of space-like surfaces, is considered. This condition leads to a new constraint for vierbein fields. Lagrangian densities leading to Frobenius's condition are given.
理論物理学刊行会の論文
1986-11-25