Accurately predicting beam-level reference signal received power (RSRP) is essential for beam management in dense multi-user wireless networks, yet challenging due to high measurement overhead and fast channel variations. This paper proposes Neural Beam Field (NBF), a hybrid neural-physical framework for efficient and interpretable spatial beam RSRP prediction. Central to our approach is the introduction of the Multi-path Conditional Power Profile (MCPP), a learnable physical intermediary representing the site-specific propagation environment. This approach decouples the environment from specific antenna/beam configurations, which helps the model learn site-specific multipath features and enhances its generalization capability. We adopt a decoupled ``blackbox-whitebox" design: a Transformer-based deep neural network (DNN) learns the MCPP from sparse user measurements and positions, while a physics-inspired module analytically infers beam RSRP statistics. To improve convergence and adaptivity, we further introduce a Pretrain-and-Calibrate (PaC) strategy that leverages ray-tracing priors for physics-grounded pretraining and then RSRP data for on-site calibration. Extensive simulation results demonstrate that NBF significantly outperforms conventional table-based channel knowledge maps (CKMs) and pure blackbox DNNs in prediction accuracy, training efficiency, and generalization, while maintaining a compact model size. The proposed framework offers a scalable and physically grounded solution for intelligent beam management in next-generation dense wireless networks.