Neural Radiance Fields (NeRF) is a powerful novel technology for the reconstruction of 3D scenes from a set of images captured by static cameras. Renders of these reconstructions could play a role in virtual presence in the operating room (OR), e.g. for training purposes. In contrast to existing systems for virtual presence, NeRF can provide real instead of simulated surgeries. This work shows how NeRF can be used for view synthesis in the OR. A depth-supervised NeRF (DS-NeRF) is trained with three or five synchronised cameras that capture the surgical field in knee replacement surgery videos from the 4D-OR dataset. The algorithm is trained and evaluated for images in five distinct phases before and during the surgery. With qualitative analysis, we inspect views synthesised by a virtual camera that moves in 180 degrees around the surgical field. Additionally, we quantitatively inspect view synthesis from an unseen camera position in terms of PSNR, SSIM and LPIPS for the colour channels and in terms of MAE and error percentage for the estimated depth. DS-NeRF generates geometrically consistent views, also from interpolated camera positions. Views are generated from an unseen camera pose with an average PSNR of 17.8 and a depth estimation error of 2.10%. However, due to artefacts and missing of fine details, the synthesised views do not look photo-realistic. Our results show the potential of NeRF for view synthesis in the OR. Recent developments, such as NeRF for video synthesis and training speedups, require further exploration to reveal its full potential.