The combination of augmented reality (AR) and medicine is an important trend in current research. The powerful display and interaction capabilities of the AR system can assist doctors to perform more complex operations. Since the tooth itself is an exposed rigid body structure, dental AR is a relatively hot research direction with application potential. However, none of the existing dental AR solutions are designed for wearable AR devices such as AR glasses. At the same time, these methods rely on high-precision scanning equipment or auxiliary positioning markers, which greatly increases the operational complexity and cost of clinical AR. In this work, we propose a simple and accurate neural-implicit model-driven dental AR system, named ImTooth, and adapted for AR glasses. Based on the modeling capabilities and differentiable optimization properties of state-of-the-art neural implicit representations, our system fuses reconstruction and registration in a single network, greatly simplifying the existing dental AR solutions and enabling reconstruction, registration, and interaction. Specifically, our method learns a scale-preserving voxel-based neural implicit model from multi-view images captured from a textureless plaster model of the tooth. Apart from color and surface, we also learn the consistent edge feature inside our representation. By leveraging the depth and edge information, our system can register the model to real images without additional training. In practice, our system uses a single Microsoft HoloLens 2 as the only sensor and display device. Experiments show that our method can reconstruct high-precision models and accomplish accurate registration. It is also robust to weak, repeating and inconsistent textures. We also show that our system can be easily integrated into dental diagnostic and therapeutic procedures, such as bracket placement guidance.