Particle production by a relativistic semitransparent mirror in (1+3)D Minkowski spacetime

Production of massless, scalar particles by a relativistic, semitransparent, plane mirror in (1 + 3)D Minkowski spacetime based on the Barton-Calogeracos (BC) action is investigated. The corresponding Bogoliubov coefficients are derived for a mirror with arbitrary, relativistic trajectories. We apply our derived formula to two specific trajectories. One is commonly used in the (1 + 1)D literature to mimic gravitational collapse theoretically, and the other is proposed to be realizable experimentally. In addition, we identify the relation between the particle spectrum and the particle production probability, and we demonstrate the equivalence between our approach and the existing approach in the literature, which is restricted to (1 + 1)D. In short, our treatment extends the study to (1 + 3)D spacetime for a relativistic, plane mirror. Lastly, we offer a third approach for finding the particle spectrum using the S-matrix formalism.