Lagrangian for the Majorana-Ahluwalia Construct

TL;DR

This paper reformulates the equations for self/anti-self charge conjugate states into a covariant Lagrangian, linking it to extended Lorentz group representations and discussing its relation to existing quantum theory concepts.

Contribution

It introduces a covariant Lagrangian for the Majorana-Ahluwalia construct based on doubled Lorentz group representations, expanding the theoretical framework for neutral particle fields.

Findings

Rewritten equations in covariant form

Proposed Lagrangian for neutral particles

Connections to extended Lorentz group representations

Abstract

The equations describing self/anti-self charge conjugate states, recently proposed by Ahluwalia, are re-written to covariant form. The corresponding Lagrangian for the neutral particle theory is proposed. From a group-theoretical viewpoint the construct is an example of the Nigam-Foldy-Bargmann-Wightman-Wigner-type quantum field theory based on the doubled representations of the extended Lorentz group. Relations with the Sachs-Schwebel and Ziino-Barut concepts of relativistic quantum theory are discussed.