A Covariant Framework for Generalized Spinor Dual Structures

Abstract

In this work, we propose a novel framework for defining the dual structure of a spinor. This construction relies on the basis elements of the Clifford algebra, leading to a covariant structure that embeds the dual. The formulation includes free parameters that may be adjusted to meet specific requirements. Remarkably, it enables the explicit construction of representatives for each class within a recently proposed general classification of spinors. In addition to recovering known results, the formalism paves the way for the development of potential new theories in a manifestly covariant setting.

9 pages

References in corpus (11)

• Spin half fermions with mass dimension one: theory, phenomenology, and dark matter
• Dark matter: A spin one half fermion field with mass dimension one?
• The theory of local mass dimension one fermions of spin one half
• An Identification of the Dirac Operator with the Parity Operator
• Revealing how different spinors can be: the Lounesto spinor classification
• Further investigation of mass dimension one fermionic duals
• On the generalized spinor classification: Beyond the Lounesto's Classification
• Non-standard Dirac adjoint spinor: The emergence of a new dual
• On Wigner Degeneracy in Elko theory: Hermiticity and Dark Matter
• Revisiting Takahashi's inversion theorem in discrete symmetry-based dual frameworks
• Spinor Adjoints, Gauge Invariance and a new Road to Sterile Neutrinos