From Hole Theory to Quantum Field Theory: Relativistic Fermions and the Role of Ettore Majorana (1933-1937)

Between 1933 and 1937, the treatment of relativistic spin-1/2 particles, initially rooted in Hole theory, evolved into the modern framework of quantum field theory. This paper reconstructs the crucial stages of that transition by examining the formal and physical progress of the numerous authors who shaped the field's modern formalism. This historical study traces the development of fermionic field theory in full, beginning with the foundational work of the 1920s, focussing on the results of the 1930s, and concluding with the influential synthesis of Wolfgang Pauli in 1941, the content of which has shaped the subsequent tradition. Within this framework, particular emphasis is given to Ettore Majorana's 1937 quantisation procedure and argument for anti-commuting fermionic quantum fields. This study demonstrates that Majorana's work was not merely a technical variant, but the definitive rejection of the concept of negative energy solutions, whose conceptual clarity and educational value remain vital today.

Source: arXiv:2603.28538v1 - http://arxiv.org/abs/2603.28538v1 PDF: https://arxiv.org/pdf/2603.28538v1 Original Link: http://arxiv.org/abs/2603.28538v1