Canonical Quantum Theory of Gravitational Field with Higher Derivatives

A renormalizable gravitational theory with higher derivatives is canonically quantized in the Landau gauge. Field equations and various equal-time commutation relations are explicitly given. The main results obtained in this work are 1) the equal-time commutation relations involving bµ exhibit the tensor-like behaviour and 2) the theory has the 16-dimensional Poincaré-like superalgebra. These results are just the same as those discovered by Nakanishi in the Einstein case.