Related papers: A first-order purely frame-formulation of General …
We present a convenient null gauge for the construction of the balanced equations of motion. This null gauge has the property that the asymptotic structure is intimately related to the interior one; in particular there is a strong connexion…
We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra $\mathfrak{g}$ leads naturally to the appearance of the "generalized tangent bundle" $\mathbb{T}M \equiv TM \oplus T^*M$…
One hundred years ago this year attempts began to generalise general relativity with the ambition of incorporating electromagnetism alongside gravitation in a unified field theory. These developments led to gauge theories and models with…
We construct a graded Lie algebra in which a solution to the vacuum Einstein equations is any element of degree 1 whose bracket with itself is zero. Each solution generates a cochain complex, whose first cohomology is linearized gravity…
A gauge theory of the Lorentz group with a mass-dimension one gauge field coupling to matter of any spin is developed. As a completely new feature the "Vierbein" assuring local gauge invariance enters not as an independent dynamical field,…
The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global…
Recently, a bundle theoretic description of massive single-particle state spaces, which is better suited for Relativistic Quantum Information Theory than the ordinary Hilbert space description, has been suggested. However, the mathematical…
We address the gravitation and inertia in the framework of 'general gauge principle', which accounts for 'gravitation gauge group' generated by hidden local internal symmetry implemented on the flat space. We connect this group to nonlinear…
By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called…
A formal symmetry between generalized coordinates and momenta is postulated to formulate classical and quantum theories of a particle coupled to an Abelian gauge field. It is shown that the symmetry (a) requires the field to have dynamic…
With the aim of deriving symmetric hyperbolic free-evolution systems for GR that possess Hamiltonian structure and allow for the popular puncture gauge condition we analyze the hyperbolicity of Hamiltonian systems. We develop helpful tools…
Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates QED. Here we formalize and generalize…
We present a generalization of the first-order formalism used to describe the dynamics of a classical system. The generalization is then applied to the first-order action that describes General Relativity. As a result we obtain equations…
In this work, we make new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this…
Gauging of space translations for nonrelativistic point particles in one dimension leads to general coordinate transformations with fixed Newtonian time. The minimal gauge invariant extension of the particle velocity requires the…
Black hole perturbation theory beyond second order is not well understood because typically one defines the meaning of gauge invariance order by order which is ambiguous. In this series of works we therefore developed a new approach which…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
The present article deals with a formulation of the so called (vacuum) Palatini gravity as a general variational principle. In order to accomplish this goal, some geometrical tools related to the geometry of the bundle of connections of the…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
G\"{o}del universe is a homogeneous rotating dust with negative $\Lambda$ which is a direct product of three dimensional pure rotation metric with a line. We would generalize it to higher dimensions for Einstein and pure Lovelock gravity…