Related papers: Absolute versus Relational Debate: a Modern Global…
Shape Dynamics (SD) is a theory dynamically equivalent to vacuum General Relativity (GR), which has a different set of symmetries. It trades refoliation invariance, present in GR, for local 3-dimensional conformal invariance. This…
There is a unique variant of Absolute Parallelism, which is very simple as it has no free parameters: nothing (nor D=5) can be changed if to keep the theory safe from emerging singularities of solutions. On the contrary, eternal solutions…
In this letter we use the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence to establish a set of old conjectures about symmetries in quantum gravity. These are that no global symmetries are possible, that internal gauge…
Shape dynamics is a completely background-independent universal framework of dynamical theories from which all absolute elements have been eliminated. For particles, only the variables that describe the shapes of the instantaneous particle…
Relational mechanics is a reformulation of mechanics (classical or quantum) for which space is relational. This means that the configuration of an $N$-particle system is a shape, which is what remains when the effects of rotations,…
We show that one can construct two equivalent gauge theories from a linking theory and give a general construction principle for linking theories which we use to construct a linking theory that proves the equivalence of General Relativity…
The notion of "reference frame" is a central theoretical construct for interpreting the physical implications of spacetime diffeomorphism invariance in General Relativity. However, the alternative formulation of classical General Relativity…
A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a…
All gauge theories need ``something fixed'' even as ``something changes.'' Underlying the implementation of these ideas all major physical theories make indispensable use of an elaborately designed spacetime model as the ``something…
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…
This work may be defined as a modern philosophical approach to theoretical physics. Since ancient times science and philosophy evolved in parallel, thus renewing from time to time the epochal paradigms of human thought. We could not…
Shape dynamics is a classical theory of gravity which agrees with general relativity in many important aspects, but which possesses different gauge symmetries and can present some fundamental global differences with respect to Einstein…
Starting with assumptions both simple and natural from "physical" point of view we present a direct construction of transformations preserving wide class of (anti)commutation relations which describe Euclidean/Minkowski superspace…
This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy…
Affine variational principle for General Relativity, proposed in 1978 by one of us (J.K.), is a good remedy for the non-universal properties of the standard, metric formulation, arising when the matter Lagrangian depends upon the metric…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…
This survey/expository article covers a variety of topics related to the "topology at infinity" of noncompact manifolds and complexes. In manifold topology and geometric group theory, the most important noncompact spaces are often…
In the paper two important theorems about complete affine spheres are generalized to the case of statistical structures on abstract manifolds. The assumption about constant sectional curvature is replaced by the assumption that the…
Compatible equations, Singularities of solutions, Topological charges and quasi-charges. PhD thesis (translated frorm Russian). The book shows the sights of Absolute Parallelism (AP), and contains useful information on the problem of…
Inspired by its fundamental importance in quantum mechanics, we define and study the notion of entanglement for abstract physical theories, investigating its profound connection with the concept of superposition. We adopt the formalism of…