# How to show that tensor gravity is nonrenormalizable?

Let's have the tensor gravity theory, which represented the massless spin-2 field: $$L = -\frac{1}{32 \pi G}\left( \frac{1}{2}(\partial_{\alpha}h_{\nu \beta}) \partial^{\alpha}\bar {h}^{\nu \beta} - (\partial^{\alpha} \bar {h}_{\mu \alpha })\partial_{\beta}\bar {h}^{\mu \beta}\right) - \frac{1}{2}\int h_{\mu \nu} (T^{\mu \nu} + \tau^{\mu \nu}),$$ where $$\bar {h}^{\mu \nu} = h^{\mu \nu} - \frac{1}{2}\eta^{\mu \nu}h^{\alpha}_{\alpha}, \quad h_{\mu \nu} = h_{\nu \mu},$$ $T_{\mu \nu}$ is the stress-energy tensor of all fields axcept gravitational field and $\tau_{\mu \nu}$ is the stress-energy tensor of the particles, $$\tau_{\mu \nu} = m\int \frac{dz^{\mu}}{d \tau}\frac{dz^{\nu}}{d \tau} \delta^{4}(x - x(\tau ))d\tau .$$ How to show that it is nonrenormalizable? Does it connect with internal inconsistency of the theory, which is connected with the statement that conservation of $\tau_{\mu \nu}$ is true if and only if the gravity field doesn't affect on the motion of particle?

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