Related papers: Complementarity of Kinematics and Geometry in Gene…
A brief summary of results on kinematic self-similarities in general relativity is given. Attention is focussed on locally rotationally symmetric models admitting kinematic self-similar vectors. Coordinate expressions for the metric and the…
For theories formulated with a maximally symmetric momentum space we propose a general characterization for the description of interactions in terms of the isometry group of the momentum space. The well known cases of…
The existence of kinematic formulas for area measures with respect to any connected, closed subgroup of the orthogonal group acting transitively on the unit sphere is established. In particular, the kinematic operator for area measures is…
We consider plane symmetric gravitational fields within the framework of General Relativity in (D+1)-dimensional spacetime. Two classes of vacuum solutions correspond to higher-dimensional generalizations of the Rindler and Taub spacetimes.…
Recently we have presented a new formulation of the theory of gravity based on an implementation of the Einstein Equivalence Principle distinct from General Relativity. The kinetic part of the theory - that describes how matter is affected…
The gravitational energy-momentum and angular momentum satisfy the algebra of the Poincare group in the full phase space of the teleparallel equivalent of general relativity. The expression for the gravitational energy-momentum may be…
We discuss equivalent representations of gravity in the framework of metric-affine geometries pointing out basic concepts from where these theories stem out. In particular, we take into account tetrads and spin connection to describe the so…
We define and study kinematical observables involving fermion spin, such as the total spin of a collection of particles, in loop quantum gravity. Due to the requirement of gauge invariance, the relevant quantum states contain strong…
A possible model for quantum kinematics of a test particle in a curved space-time is proposed. Every reasonable neighbourhood V_e of a curved space-time can be equipped with a nonassociative binary operation called the geodesic…
A reference frame consists of: a reference space, a time scale and a spatial metric. The geometric structure induced by these objects in spacetime is developed. The existence of a class of spatial metrics that are rigid, have free mobility…
Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations that are predictive, interpretable and quantizable. These three conditions on matter translate…
We explore the geometrical meaning of teleparallel geometries and the role of covariance in their definition. We argue that pure gauge connections are a necessary ingredient for describing geometry and gravity in terms of torsion and…
We present our Finsler spacetime formalism which extends the standard formulation of Finsler geometry to be applicable in physics. Finsler spacetimes are viable non-metric geometric backgrounds for physics; they guarantee well defined…
We analyse the Finsler geometries of the kinematic space of spinless and spinning electrically charged particles in an external Ra\~{n}ada field. We consider the most general actions that are invariant under the Lorentz, electromagnetic…
A new formulation of relativistic quantum mechanics is presented and applied to a free, massive, and spin zero elementary particle in the Minkowski spacetime. The reformulation requires that time and space, as well as the timelike and…
The algebra of biquaternions possess a manifestly Lorentz invariant form and induces an extended space-time geometry. We consider the links between this complex pre-geometry and real geometry of the Minkowski space-time. Twistor structures…
We discuss the conditions for mapping the geometric description of the kinematics of particles that probe a given Hamiltonian in phase space to a description in terms of Finsler geometry (and vice-versa).
An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after…
The first part of this work deals with the development of a natural differential calculus on non-commutative manifolds. The second part extends the covariance and equivalence principle as well studies its kinematical consequences such as…
A covariant hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of hamiltonians accounting for specific properties and…