The Pinching-Antenna SyStem (PASS) is a revolutionary flexible antenna technology designed to enhance wireless communication by establishing strong line-of-sight (LoS) links, reducing free-space path loss and enabling antenna array reconfigurability. PASS uses dielectric waveguides with low propagation loss for signal transmission, radiating via a passive pinching antenna, which is a small dielectric element applied to the waveguide. This paper first proposes a physics-based hardware model for PASS, where the pinching antenna is modeled as an open-ended directional coupler, and the electromagnetic field behavior is analyzed using coupled-mode theory. A simplified signal model characterizes the coupling effect between multiple antennas on the same waveguide. Based on this, two power models are proposed: equal power and proportional power models. Additionally, a transmit power minimization problem is formulated/studied for the joint optimization of transmit and pinching beamforming under both continuous and discrete pinching antenna activations. Two algorithms are proposed to solve this multimodal optimization problem: the penalty-based alternating optimization algorithm and a low-complexity zero-forcing (ZF)-based algorithm. Numerical results show that 1) the ZF-based low-complexity algorithm performs similarly to the penalty-based algorithm, 2) PASS reduces transmit power by over 95% compared to conventional and massive MIMO, 3) discrete activation causes minimal performance loss but requires a dense antenna set to match continuous activation, and 4) the proportional power model yields performance comparable to the equal power model.