Spin-Vector Gauge Fields in the Gauge Theory of Gravity

Abstract

The gauge theory of gravity based on the 4-dimensional super translation group ST_I^4 is investigated. The algebra of ST_I^4 is constructed by the differential operators in spin vector space and resembles to super slgebra, although Grassmann coordinates are not introduced. There appears anti-commuting spin vector gauge fields ω_a^A (A=1,2), which are the analogues of the vierbein fields b_a^i (i=0〜3). The ghost fields ca for the general coordinate transformation and the metric tensor Gab in the bundle space include the spin vector gauge fields ω_a-A as well as the soldering forms σ_a^<AB'>. The matching condition on two overlapping charts can be solved perturbatively and then the extended connection is consistently defined in the bundle space.