Symmetries and causes of the coincidence of the emission spectra of mirrors and charges in 1+1 and 3+1 spaces

This paper discusses the symmetry of the wave field that lies to the right and left of a two-sided accelerated mirror in 1+1 space and satisfies a single condition on it. The symmetry is embodied in the Bogolyubov matrix coefficients α and β that connect the two complete sets of solutions of the wave equations. The amplitudes of the quantum processes in the right and left half-spaces are expressed in terms of α and β and are related to each other by the transformation (12). The coefficient β _ω′ω ^* plays the role of the source amplitude of a pair of oppositely directed particles with frequencies ω and ω′ of which one is in the left half-space and the other is in the right half-space because one of them has undergone reflection. Such an interpretation makes β _ω′ω ^* observable and explains why, as shown by Eq. (1) and found earlier by Nikishov and Ritus Zh. éksp. Teor. Fiz. 108, 1121 (1995); transl. JETP 81, 615 (1995)] and by Ritus Zh. éksp. Teor. Fiz. 110, 526 (1996); transl. JETP 83, 282 (1996)], the emission spectra of a mirror in 1+1 space coincide with those of charges in 3+1 space. The reason is that the angular momentum of the pair emitted by the mirror coincides with the angular momentum of the single particle emitted by the charge. Zh. éksp. Teor. Fiz. 114, 46–62 (July 1998)