Related papers: Gauge Formalism for General Relativity and Fermion…
A general theory of quantum spinor structures on quantum spaces is presented, within the conceptual framework of the formalism of quantum principal bundles. Quantum analogs of all basic objects of the classical theory are constructed and…
Spinors have played an essential but enigmatic role in modern physics since their discovery. Now that quantum-gravitational theories have started to become available, the inclusion of a description of spin in the development is natural and…
The classical theory of gravity is formulated as a gauge theory on a frame bundle with spontaneous symmetry breaking caused by the existence of Dirac fermionic fields. The pseudo-Riemannian metric (tetrad field) is the corresponding Higgs…
A unified description of all interactions could be based on a higher-dimensional theory involving only spinor fields. The metric arises as a composite object and the gravitational field equations contain torsion-corrections as compared to…
The fundamental concepts of Riemannian geometry, such as differential forms, vielbein, metric, connection, torsion and curvature, are generalized in the context of non-commutative geometry. This allows us to construct the…
We introduce in the framework of the linear approximation of General relativity a natural distinction between General gauge transformations generated by any vector field and those Special ones for which this vector field is a gradient. This…
Quantum theory is formulated as a probabilistic theory on a flat Minkowski space-time, while general theory of relativity is formulated on a curved manifold as a geometric theory. Bohmian Quantum Gravity approach indicates that one need to…
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…
As in the case of the other gauge field theories, there is so called ``gauge'' also in general relativity. This ``gauge'' is unphysical degree of freedom. There are two kinds of ``gauges'' in general relativity. These are called the first-…
Field theoretic models possessing a global internal fermionic shift symmetry are considered. When such a symmetry is realized locally, spin 3/2 fields appear naturally as gauge fields. Implementation of the gauging procedure requires not…
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge…
We develop a gauge-invariant formalism to describe metric perturbations in five-dimensional brane-world theories. In particular, this formalism applies to models originating from heterotic M-theory. We introduce a generalized longitudinal…
Higher spin tensor gauge fields have natural gauge-invariant field equations written in terms of generalised curvatures, but these are typically of higher than second order in derivatives. We construct geometric second order field equations…
General Relativity can be formulated in terms of a spatially Weyl invariant gauge theory called Shape Dynamics. Using this formulation, we establish a "bulk/bulk" duality between gravity and a Weyl invariant theory on spacelike Cauchy…
In this paper we investigate the Yokoyama gaugeon formalism for perturbative quantum gravity in a general curved spacetime. Within the gaugeon formalism, we extend the configuration space by introducing vector gaugeon fields describing a…
Two-spinor formalism for Einstein Lagrangian is developed. The gravitational field is regarded as a composite object derived from soldering forms. Our formalism is geometrically and globally well-defined and may be used in virtually any…
Classical gravitation theory is formulated as gauge theory on natural bundles where gauge symmetries are general covariant transformations and a gravitational field is a Higgs field responsible for their spontaneous symmetry breaking.
The following two loosely connected sets of topics are reviewed in these lecture notes: 1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall…
We explore new aspects of internal fermionic shifting symmetries, present in physical systems such as free Dirac spinors and p-form tensor-spinor fields. We propose a novel procedure to gauge these global symmetries, which also introduces a…
The purpose of this paper is to present a generalized hole argument for gauge field theories and their geometrical setting in terms of fiber bundles. The generalized hole argument is motivated and extended from the spacetime hole arguments…