Flag-dipole spinors: On the dual structure derivation and $\mathcal{C}$, $\mathcal{P}$ and $\mathcal{T}$ symmetries

Unveiling a spinor field classification with non-Abelian gauge symmetries

A spinor fields classification with non-Abelian gauge symmetries is introduced, generalizing the the U(1) gauge symmetries-based Lounesto's classification. Here, a more general classification, contrary to the Lounesto's one, encompasses spinor multiplets, corresponding to non-Abelian gauge fields. The particular case of SU(2) gauge symmetry, encompassing electroweak and electromagnetic conserved charges, is then implemented by a non-Abelian spinor classification, now involving 14 mixed classes of spinor doublets. A richer flagpole, dipole, and flag-dipole structure naturally descends from this…

旋量的几何：双重手征平面波展开

Geometry of spinors: doubly-chiral plane-wave expansion

本文采用旋量场的极坐标重构，重新审视旋量分类并研究旗杆子类作为 Dirac 场方程解的条件，进而提出对平面波展开的扩充。

The emergence of flagpole and flag-dipole fermions in fluid/gravity correspondence

The emergence of flagpole and flag-dipole singular spinor fields is explored, in the context of fermionic sectors of fluid/gravity correspondence, arising from the duality between the gravitino, in supergravity, and the phonino, in supersymmetric hydrodynamics. Generalized black branes, whose particular case consists of the AdS--Schwarzschild black brane, are regarded. The correspondence between hydrodynamic transport coefficients, and the universal absorption cross sections of the generalized black branes, is extended to fermionic sectors, including supersound diffusion constants. A free para…

无质量散射的奇点与cluster algebras（簇代数）

Singularities of massless scattering and cluster algebras

本研究探讨无质量散射运动学中部分旗簇关联的簇代数，验证其包含非对偶共形无质量散射振幅相关信息，对比五点、六点下旋量-螺旋度与动量扭量簇结构的符号字母表捕获能力，并发现簇结构可预测相关符号字母三元组的出现。

Twistors, Generalizations and Exceptional Structures

This paper is intended to describe twistors via the paravector model of Clifford algebras and to relate such description to conformal maps in the Clifford algebra over R(4,1), besides pointing out some applications of the pure spinor formalism. We construct twistors in Minkowski spacetime as algebraic spinors associated with the Dirac-Clifford algebra, using one lower spacetime dimension than standard Clifford algebra formulations, since for this purpose the Clifford algebra over R{4,1} is also used to describe conformal maps, instead of R{2,4}. It is possible to identify the twistor fiber in …

A derivation of the Breit equation from Barut's covariant formulation of electrodynamics in terms of direct interactions

We study Barut's covariant equations describing the electromagnetic interactions between N spin-1/2 particles. In the covariant formulation each particle is described by a Dirac spinor. It is assumed that the interactions between the particles are not mediated by a bosonic field (direct interactions). Within this formulation, using the Lagrangian formalism, we derive the approximate (semirelativistic) Breit equation for two interacting spin-1/2 particles.

Symplectic Dolbeault Operators on Kähler Manifolds

For a Kähler Manifold $M$, the "symplectic Dolbeault operators" are defined using the symplectic spinors and associated Dirac operators, in complete analogy to how the usual Dolbeault operators, $\bar\partial$ and $\bar\partial^*$, arise from Dirac operators on the canonical complex spinors on $M$. We give special attention to two special classes of Kähler manifolds: Riemann surfaces and flag manifolds ($G/T$ for $G$ a simply-connected compact semisimple Lie group and $T$ a maximal torus). In the case of flag manifolds, we work with the Hermitian structure induced by the Killing form and a cho…

The algebraic structure of Galilean superconformal symmetries

The semisimple part of d-dimensional Galilean conformal algebra g^(d) is given by h^(d)=O(2,1)+O(d), which after adding via semidirect sum the 3d-dimensional Abelian algebra t^(d) of translations, Galilean boosts and constant accelerations completes the construction. We obtain Galilean superconformal algebra G^(d) by firstly defining the semisimple superalgebra H^(d) which supersymmetrizes h^(d), and further by considering the expansion of H^(d) by tensorial and spinorial graded Abelian charges in order to supersymmetrize the Abelian generators of t^(d). For d=3 the supersymmetrization of h^(3…