相关论文: Formulation of spinors in terms of gauge fields

We present a simple, systematic and practical method to construct conformally invariant equations in arbitrary Riemann spaces. This method that we call "Weyl-to-Riemann" is based on two features of Weyl geometry. i) A Weyl space is defined…

Building on the universal covering group of the general linear group, we introduce the composite spinor bundle whose subbundles are Lorentz spin structures associated with different gravitational fields. General covariant transformations of…

In the standard model, electroweak theory is based on chiral gauge symmetry, which only contains massless fermions and gauge vectors. So the fundamental field equations are Weyl equations including gauge vectors. We deduced these Weyl…

A gauge theory of the Lorentz group, based on the different behavior of spinors and vectors under local transformations, is formulated in a flat space-time and the role of the torsion field within the generalization to curved space-time is…

We extend our program, of coupling theories to scale in order to make their Weyl invariance manifest, to include interacting theories, fermions and supersymmetric theories. The results produce mass terms coinciding with the standard ones…

Linear spinor fields are a generalization of the Dirac field that have direct correspondence with the known physics of fermions, inherent causality properties in their most fundamental constructions, and positive mass eigenvalues for all…

We consider the wave equation for spinors in ${\cal D}$-dimensional Weyl geometry. By appropriately coupling the Weyl vector $\phi _{\mu}$ as well as the spin connection $\omega _{\mu a b } $ to the spinor field, conformal invariance can be…

We present a unified framework demonstrating how the spinor complex Lorentz group SL(2,C)/Z\_2 is realized as a canonical subgroup within a four-dimensional complex Riemannian manifold. Building on the complex, holomorphic metric extension…

In gravitation theory, the realistic fermion matter is described by spinor bundles associated with the cotangent bundle of a world manifold $X$. In this case, the Dirac operator can be introduced. There is the 1:1 correspondence between…

A review of some facts concerning classical spacetime geometry is presented together with a description of the most elementary aspects of the two-component spinor formalisms of Infeld and van der Waerden. Special attention is concentrated…

In spinor formalism, since any massless free-field spinor with spin higher than $1/2$ can be constructed with spin-1/2 spinors (Dirac-Weyl spinors) and scalars, we introduce a map between Weyl fields and Dirac-Weyl fields. We determine the…

Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It…

A spinor current-source is found in the Weyl non-Abelian gauge theory which does not contain the abstract gauge space. It is shown that the searched spinor representation can be constructed in the space of external differential forms and it…

The unique off-shell fermionic gauge invariance of a vector-spinor field theory is found, and the invariant action is derived. The latter is Weyl invariant in any dimension in the massless limit, and it coincides with the singular point of…

We consider modified Weyl gravity where a Dirac spinor field is nonminimally coupled to gravity. It is assumed that such modified gravity is some approximation for the description of quantum gravitational effects related to the gravitating…

We present a geometrical unification theory in a Kaluza-Klein approach that achieve the geometrization of a generic gauge theory bosonic component. We show how it is possible to derive the gauge charge conservation from the invariance of…

Holonomy algebras of Lorentzian Weyl spin manifolds with weighted parallel spinors are found. For Lorentzian Weyl manifolds admitting recurrent null vector fields are introduced special local coordinates similar to Kundt and Walker ones.…

A spinorial approach to 6-dimensional differential geometry is constructed and used to analyze tensor fields of low rank, with special attention to the Weyl tensor. We perform a study similar to the 4-dimensional case, making full use of…

We introduce a novel spinorial description for the higher-spin gauge theory induced by the IKKT matrix model on an FLRW spacetime with Lorentzian signature, called Lorentzian $\mathfrak{hs}$-IKKT theory. The new description is based on Weyl…

A massless Weyl-invariant dynamics of a scalar, a Dirac spinor, and electromagnetic fields is formulated in a Weyl space, $W_4$, allowing for conformal rescalings of the metric and of all fields with nontrivial Weyl weight together with the…