Electrical impedance tomography (EIT) reconstructs the internal conductivity distribution from boundary voltage measurements induced by current excitation. However, its inverse problem is severely ill-posed. Conventional reconstruction methods generally suffer from low spatial resolution, whereas deep learning approaches can substantially improve image quality but rely heavily on paired voltage-conductivity data. This paper proposes a self-supervised learning EIT method with physics-informed priors and coordinate-conditioned neural representation. Built upon a first-order forward physical model, the proposed method establishes forward and backward cycle-consistency constraints between the image domain and the measurement domain, thereby enabling network training with unpaired data. To enhance the representation of continuous image domain and improve target boundary detail recovery, a coordinate-conditioned image generation network is developed. Specifically, the voltage sequence is reorganized as a pseudo-image for local feature extraction through convolutional layers, after which conductivity values are predicted pixel by pixel by jointly integrating global voltage features and coordinate-based positional encoding. In addition, a boundary consistency constraint and an adversarial learning strategy are introduced to further improve the structural fidelity of reconstructed images. The reconstruction results demonstrate that the proposed method outperforms other traditional and self-supervised learning methods in target localization, shape recovery, and artifact suppression. On the simulation dataset, the average correlation coefficient (CC), root mean square error (RMSE), and structural similarity index (SSIM) of the proposed method are 0.919, 0.099, and 0.812, respectively. Compared with the most competitive baseline in the phantom experiments, the proposed method improves the average CC by 0.043, reduces the RMSE by 0.027, and increases the SSIM by 0.037 7. Moreover, the proposed method exhibits good robustness under noise conditions and enables high-quality image reconstruction without paired labeled data.