Related papers: Gauge Formalism for General Relativity and Fermion…
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…
We develop a frame and dyad gauge-independent formalism for the calculus of variations of functionals involving spinorial objects. As part of this formalism we define a modified variation operator which absorbs frame and spin dyad gauge…
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…
Gauge field theories may quite generally be defined as describing the coupling of a matter-field to an interaction-field, and they are suitably represented in the mathematical framework of fiber bundles. Their underlying principle is the…
The fundamental interactions of nature, the electroweak and the quantum chromodynamics, are described in the Standard Model by the Gauge Theory under internal symmetries that maintain the invariance of the functional action. The fundamental…
We present a parameter-free gauge formulation of general relativity in terms of a new set of real spin connection variables. The theory is constructed by extending the phase space of the recently formulated conformal geometrodynamics for…
It is shown how to write the first order action for gravity in a gauge theoretic formalism where the spin connection and frame field degrees of freedom are assimilated together into a gauge connection. It is then shown how to couple the…
The underlying mathematical structures of gauge theories are known to be geometrical in nature and the local and global features of this geometry have been studied for a long time in mathematics under the name of fibre bundles. It is now…
Possible geometric frameworks for a unified theory of gravity and electromagnetism are investigated: General relativity is enlarged by allowing for an arbitrary complex linear connection and by constructing an extended spinor derivative…
In gravitation theory, a fermion field must be regarded only in a pair with a certain tetrad gravitational field. These pairs can be represented by sections of the composite spinor bundle $S\to\Si\to X^4$ where values of gravitational…
The standard model ascribes distinct properties to different chiralities of fermions. We show how to incorporate this aspect in an extended spacetime-property framework involving two different attributes using a generalized metric which…
We review the basic elements of the geometrical formalism for description of gauge fields and the theory of invariant connections, and their applications to the coset space dimensional reduction of Yang-Mills theories. We also discuss the…
We show that loop gravity can equally well be formulated in in terms of spinorial variables (instead of the group variables which are commonly used), which have recently been shown to provide a direct link between spin network states and…
In classical field theory, the composite fibred manifolds Y -> Z -> X provides the adequate mathematical formulation of gauge models with broken symmetries, e.g., the gauge gravitation theory. This work is devoted to connections on…
Gravitation theory is formulated as gauge theory on natural bundles with spontaneous symmetry breaking where gauge symmetries are general covariant transformations, gauge fields are general linear connections, and Higgs fields are…
Some mathematical aspects of using the translation group as an internal symmetry group in a gauge field theory are presented and discussed. The traditional manner in which gravitation can be accounted for by the introduction of a global…
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…
In this paper connections between different gauge-theoretical problems in high and low dimensions are established. In particular it is shown that higher dimensional asd equations on total spaces of spinor bundles over low dimensional…
While general relativity provides a complete geometric theory of gravity, it fails to explain the other three forces of nature, i.e., electromagnetism and weak and strong interactions. We require the quantum field theory (QFT) to explain…
The conformal compensator formalism is a convenient and versatile representation of supergravity (SUGRA) obtained by gauge fixing conformal SUGRA. Unfortunately, practical calculations often require cumbersome manipulations of component…