Additional Equations Derived from the Ryder Postulates in the (1/2,0)+(0,1/2) Representation of the Lorentz Group

TL;DR

This paper derives second-order equations for particles in the (1/2,0)+(0,1/2) Lorentz group representation, extending previous work and providing insights into mass and spin states, with potential generalization to multiple lepton families.

Contribution

It introduces new second-order equations for the (1/2,0)+(0,1/2) representation, building on historical proposals and offering a generalized procedure for multiple lepton families.

Findings

Derived second-order equations for particle representations.

Provided insights into mass and spin state structures.

Suggested generalization to arbitrary lepton families.

Abstract

Developing recently proposed constructions for the description of particles in the $(1/2,0)\oplus (0,1/2)$ representation space, we derive the second-order equations. The similar ones were proposed in the sixties and the seventies in order to understand the nature of various mass and spin states in the representations of the $O(4,2)$ group. We give some additional insights into this problem. The used procedure can be generalized for {\it arbitrary} number of lepton families.