Unveiling Mapping Structures of Spinor Duals

Abstract

Following the program of investigation of alternative spinor duals potentially applicable to fermions beyond the standard model, we demonstrate explicitly the existence of several well-defined spinor duals. Going further we define a mapping structure among them and the conditions under which sets of such dual maps do form a group. We also study the covariance of bilinear quantities constructed with the several possible duals, the invariant eigenspaces of those group elements and its connections with spinors classification, as well as dual maps defined as elements of group algebras.

arXiv comment11 pages, no figures

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Cited by in corpus (16)

• Mass dimension one fermions: Constructing darkness
• Polar Form of Spinor Fields from Regular to Singular: the Flag-Dipoles
• Regular spinors and fermionic fields
• A new class of mass dimension one fermions
• On Wigner Degeneracy in Elko theory: Hermiticity and Dark Matter
• Spinorial discrete symmetries and adjoint structures
• Revisiting Takahashi's inversion theorem in discrete symmetry-based dual frameworks
• Flag-dipole spinors: On the dual structure derivation and $\mathcal{C}$, $\mathcal{P}$ and $\mathcal{T}$ symmetries
• Elko and Mass Dimension One Fermions: Editorial
• Singular spinors as expansion coefficients of local spin-half fermionic and bosonic fields: On the two-fold Wigner degeneracy
• Spinor Adjoints, Gauge Invariance and a new Road to Sterile Neutrinos
• General Spin Sums in Quantum Field Theory
• A note on hidden classes in spinor classification
• The Most General Propagator in Quantum Field Theory
• New constrained generalized Killing spinor field classes in warped flux compactifications
• Unraveling the Physical Meaning Behind Elko's Dual structure