Exploring a Tractable Lagrangian for Arbitrary Spin

TL;DR

This paper introduces a simple, unified Lagrangian framework capable of deriving field equations for particles of any spin, including well-known cases like Klein-Gordon, Dirac, and Proca, and discusses its symmetries and quantization.

Contribution

It proposes a universal Lagrangian approach for arbitrary spin fields, unifying various spin equations within a single formalism.

Findings

Derived field equations for arbitrary spin from the proposed Lagrangian.

Showed how Klein-Gordon, Dirac, and Proca equations emerge as special cases.

Discussed symmetries, quantization, and Feynman rules for the fields.

Abstract

A simple Lagrangian is proposed that by the choice of the representation of SU(2), gives rise to field equations for arbitrary spin. In explicit examples it is shown, how the Klein-Gordon, the Dirac, and the Proca equation can be obtained from this Lagrangian. On the same footing, field equations for arbitrary spin are given. Finally, symmetries are discussed, the fields are quantized, their statistics is deduced, and Feynman rules are derived.