Related papers: Trans-Coordinate Physics
We extend the notion of general coordinate invariance to many-body, not necessarily relativistic, systems. As an application, we investigate nonrelativistic general covariance in Galilei-invariant systems. The peculiar transformation rules…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter…
We investigate the cosmological background evolution and perturbations in a general class of spatially covariant theories of gravity, which propagates two tensor modes and one scalar mode. We show that the structure of the theory is…
Local observables in (perturbative) quantum gravity are notoriously hard to define, since the gauge symmetry of gravity -- diffeomorphisms -- moves points on the manifold. In particular, this is a problem for backgrounds of high symmetry…
A gauge-invariant wave equation for the dynamics of hybrid quantum-classical systems is formulated by combining the variational setting of Lagrangian paths in continuum theories with Koopman wavefunctions in classical mechanics. We identify…
We study the conditions of integrability when the boundary terms are considered in the variation of the geometric contribution of the Einstein-Hilbert action. We explore the emergent physical dynamics that is obtained when we make a…
Trace-free Einstein gravity is a prominent alternative to general relativity, which has two versions: one in which the energy-momentum conservation is assumed a priori and another in which it is not. In the first version, the cosmological…
We review (and extend) the analysis of general theories of all interactions (gravity included) where the mass scales are due to dimensional transmutation. Quantum consistency requires the presence of terms in the action with four…
We discuss the implications of a wave function for quantum gravity, which involves nothing but 3-dimensional geometries as arguments and is invariant under general coordinate transformations. We derive an analytic wave function from the…
A consistent implementation of quantum gravity is expected to change the familiar notions of space, time and the propagation of matter in drastic ways. This will have consequences on very small scales, but also gives rise to correction…
We construct invariant differential operators acting on sections of vector bundles of densities over a smooth manifold without using a Riemannian metric. The spectral invariants of such operators are invariant under both the diffeomorphisms…
After establishing the positivity constraint and spin content of the theory for gravitons interacting with a necessarily, and \textit{a priori}, \textit{non}-conserved external energy-momentum tensor, the expectation value formalism of the…
The covariance group for general relativity, the diffeomorphisms, is replaced by a group of coordinate transformations which contains the diffeomorphisms as a proper subgroup. The larger group is defined by the assumption that all observers…
Under the classical non-relativistic consideration of the space-time we propose the model of the laws of gravity and Electrodynamics, invariant under the galilean transformations and moreover, under every change of non-inertial cartesian…
A theory of special inconstancy, in which some fundamental physical constants such as the fine-structure and gravitational constants may vary, is proposed in pregeometry. In the special theory of inconstancy, the \alpha-G relation of…
The Gauss-Bonnet invariant connects foundational aspects of geometry with physical phenomena in a variety of ways. Teleparallel gravity offers a novel direction in which to use the Gauss-Bonnet invariant to go beyond standard cosmology. In…
The second-order moment quantum fluctuations or uncertainties are mass-dependent, and the incompatibility between the quantum uncertainty principle and the equivalence principle is at the second-order moment (variation) level, but not the…
Commuting and noncommuting space-time coordinates in a class of deformed special relativity theories are investigated. Their momentum space representation, transformation behaviour, space-time algebra, invariants and the corresponding field…
We study the variational principle over an Hilbert-Einstein like action for an extended geometry taking into account torsion and non-metricity. By extending the semi-Riemannian geometry, we obtain an effective energy-momentum tensor which…