Quantum theory of the infinite-component Majorana field and the relation of spin and statistics

Abstract

The quantum theory of the infinite-component Majorana field is formulated. The present paper discusses the three classes (slower than light, lightlike, and faster than light) of solutions to this equation and their Wigner classification. Particular attention is paid to the question of the normalization of the faster-than-light solutions. The current operator is shown to be timelike even for the spacelike solutions, and it is shown to lead to a finite process of emission of light by charged Majorana particles. The quantum theory of the Majorana field is formulated in accordance with the substitution law, and the usual connection between spin and statistics is recovered.