Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

On the Group-Theoretical Approach to Relativistic Wave Equations for Arbitrary Spin

Version 1 : Received: 20 March 2021 / Approved: 22 March 2021 / Online: 22 March 2021 (12:38:41 CET)

How to cite: Nanni, L. On the Group-Theoretical Approach to Relativistic Wave Equations for Arbitrary Spin. Preprints 2021, 2021030532 (doi: 10.20944/preprints202103.0532.v1). Nanni, L. On the Group-Theoretical Approach to Relativistic Wave Equations for Arbitrary Spin. Preprints 2021, 2021030532 (doi: 10.20944/preprints202103.0532.v1).

Abstract

Formulating a relativistic equation for particles with arbitrary spin remains an open challenge in theoretical physics. In this study, the main algebraic approaches used to generalize the Dirac and Kemmer–Duffin equations for particles of arbitrary spin are investigated. It is proved that an irreducible relativistic equation formulated using spin matrices satisfying the commutation relations of the de Sitter group leads to inconsistent results, mainly as a consequence of violation of unitarity and the appearance of a mass spectrum that does not reflect the physical reality of elementary particles. However, the introduction of subsidiary conditions resolves the problem of unitarity and restores the physical meaning of the mass spectrum. The equations obtained by these approaches are solved and the physical nature of the solutions is discussed.

Subject Areas

relativistic wave equations; higher spin; de Sitter group; irreducible representations of Lorentz group

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