Related papers: Twisted Gauge Theories
A quadratic Leibniz algebra $(\mathbb{V},[ \cdot, \cdot ],\kappa)$ gives rise to a canonical Yang-Mills type functional $S$ over every space-time manifold. The gauge fields consist of 1-forms $A$ taking values in $\mathbb{V}$ and 2-forms…
We analyse the dynamical properties of disformally transformed theories of gravity. We show that disformal transformation typically introduces novel degrees of freedom, equivalent to the mimetic dark matter, which possesses a Weyl-invariant…
We give a pedagogical account of noncommutative gauge and gravity theories, where the exterior product between forms is deformed into a $\star$-product via an abelian twist (e.g. the Groenewold-Moyal twist). The Seiberg-Witten map between…
We consider the construction of gauge theories of gravity, focussing in particular on the extension of local Poincar\'e invariance to include invariance under local changes of scale. We work exclusively in terms of finite transformations,…
The interplay between derivations and algebraic structures has been a subject of significant interest and exploration. Inspired by Yau's twist and the Leibniz rule, we investigate the formal deformation of twisted Lie algebras by invertible…
Deformation theory refers to an apparatus in many parts of math and physics for going from an infinitesimal (= first order) deformation to a full deformation, either formal or convergent appropriately. If the algebra being deformed is that…
In the first part, we discuss the interplay between local scale invariance and metric-affine degrees of freedom from few distinct points of view. We argue, rather generally, that the gauging of Weyl symmetry is a natural byproduct of…
The importance of the first-class constraint algebra of general relativity is not limited just by its self-contained description of the gauge nature of spacetime, but it also provides conditions to properly evolve the geometry by selecting…
A covariant formalism for Moyal deformations of gauge theory and differential equations which determine Seiberg-Witten maps is presented. Replacing the ordinary product of functions by the noncommutative Moyal product, noncommutative…
The construction of conformally invariant gauge conditions for Maxwell and Einstein theories on a manifold M is found to involve two basic ingredients. First, covariant derivatives of a linear gauge (e.g. Lorenz or de Donder), completely…
In the usual approach to q-deformed gauge theories, the gauge fields are required to be non-local or non-commutative one's. If we introduce, however, an extended product, which we call `` $\star$-product\rq\rq, among the generators of a…
We examine some issues that arise in the q-deformation of a gauge theory. If the deformation is carried out by replacing the equal time commutators of free fields by the corresponding q-commutators, the resulting propagators are not very…
On the basis of the general principles of a gauge field theory the gauge theory for the Poincar\'{e}-Weyl group is constructed. It is shown that tetrads are not true gauge fields, but represent functions from true gauge fields: Lorentzian,…
Any deformation of a Weyl or Clifford algebra can be realized through a change of generators in the undeformed algebra. q-Deformations of Weyl or Clifford algebrae that were covariant under the action of a simple Lie algebra g are…
We discuss conservation laws for gravity theories invariant under general coordinate and local Lorentz transformations. We demonstrate the possibility to formulate these conservation laws in many covariant and noncovariant(ly looking) ways.…
The field equations of noncommutative gravity can be obtained by replacing all exterior products by twist-deformed exterior products in the action functional of general relativity, and are here studied by requiring that the torsion 2-form…
We describe gauge theories which allow to retrieve a large class of gravitational theories, including, MacDowell-Mansouri gravity and its topological extension to Loop Quantum Gravity via the Pontrjagin characteristic class involving the…
The field equations in modified gravity theories possess an important decoupling property with respect to certain classes of nonholonomic frames. This allows us to construct generic off--diagonal solutions depending on all spacetime…
This paper shows how gauge theoretic structures arise naturally in a non-commutative calculus. Aspects of gauge theory, Hamiltonian mechanics and quantum mechanics arise naturally in the mathematics of a non-commutative framework for…
In this work a tetrad theory of gravity, invariant under conformal transformations, is investigated. The action of the theory is similar to the action of Maxwell's electromagnetism. The role of the electromagnetic gauge potential is played…