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

TL;DR

This paper explores the symmetry properties of wave fields around accelerated mirrors in 1+1 space and relates these to radiation spectra similarities with charges in 3+1 space, highlighting the role of Bogolyubov coefficients.

Contribution

It introduces a symmetry framework for wave fields near accelerated mirrors and links quantum process amplitudes to observable pair production phenomena, explaining spectral coincidences.

Findings

Symmetry of wave fields is characterized by Bogolyubov matrix coefficients.

The coefficient β* acts as a source amplitude for particle pairs.

Radiation spectra of mirrors in 1+1 space match those of charges in 3+1 space due to pair emission properties.

Abstract

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 accumulated in the Bogolyubov matrix coefficients $\alpha$ and $\beta$ 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 $\alpha$ and $\beta$ and are related to each other by transformation (12). Coefficient $\beta_{\omega'\omega}^*$ plays the role of the source amplitude of a pair of particles that are directed to opposite sides with frequencies $\omega$ and $\omega'$ but that are in either the left or the right half-space as a consequence of the reflection of one of them. Such an interpretation makes $\beta_{\omega'\omega}^*$ observable and explains the equalities, given by Eq. (1) and found earlier by Nikishov and author [Zh. Eksp. Teor. Fiz. 108, 1121 (1995)] and by author [Zh. Eksp. Teor. Fiz. 110, 526 (1996)] that the radiation spectra of a mirror in 1+1 space coincide with those of charges in 3 + 1 space by the fact that the moment of the pair emitted by the mirror coincide with the spin of the single particle emitted by the charge.