Non-standard Dirac adjoint spinor: The emergence of a new dual

TL;DR

This paper introduces a novel derivation of the Dirac dual structure using a different mathematical approach, aiming to create an alternative dual that preserves invariant norms under SL(2,C) transformations and maintains physical content.

Contribution

It proposes a new method for deriving the Dirac dual, resulting in an alternative dual structure that preserves invariance and physical properties, challenging the traditional formulation.

Findings

Successfully derived a new Dirac dual structure

Preserves invariant norms under SL(2,C) transformations

Maintains the physical content of Dirac spinors

Abstract

In this present communication we provide a new derivation of the Dirac dual structure by employing a different approach from the originally proposed. Following a general and rigorous mathematical process to compute the dual structure, we investigate if is possible to break the existing "rigidity" in its primordial formulation. For this task, firstly, we look towards to understand the core of the Dirac spinors construction and then, we suggest to built an alternative dual structure for the Dirac spinor, which preserve an invariant norm under any $SL(2,\mathcal{C})$ transformation. Finally, we verify if the prominent physical contents are maintained or if it is affected by such construction.