We introduce new techniques that can preserve unitarity of the system including ghost particles. Negative norms of the particles can be involved in zero-norm states by constraints of the physical space. These are useful to apply the higher-derivative propagator for quantum gravity to suppress divergences of vacuum energy and graviton mass correction. The quantum effects are mainly depending on the ghost mass scale. As the scale can be chosen in any order, the observed cosmological constant is realized. Further, applying ghost partners for the standard model particles, quantum gravity with matter fields becomes renormalizable with power counting arguments.
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