Related papers: Action Principle for Scale Invariance and Applicat…
In contrast to the symmetries of translation in space, rotation in space, and translation in time, the known laws of physics are not universally invariant under transformation of scale. However, the action can be invariant under change of…
Scale invariance in the theory of classical mechanics can be induced from the scale invariance of background fields. In this paper we consider the relation between the scale invariance and the constants of particle motion in a self-similar…
Galaxy velocities in clusters, rotation curves of galaxies, and "vertical" oscillations in the Milky Way currently show too high velocities with respect to the masses thought to be involved. While these velocity excesses are currently…
We present the most general actions of a single scalar field and two scalar fields coupled to gravity, consistent with second order field equations in four dimensions, possessing local scale invariance. We apply two different methods to…
Scale invariance is considered in the context of gravitational theories where the action, in the first order formalism, is of the form $S = \int L_{1} \Phi d^4x$ + $\int L_{2}\sqrt{-g}d^4x$ where the volume element $\Phi d^4x$ is…
The source of the acceleration of the expansion of the Universe is still unknown. We examine some consequences of the possible scale invariance of the empty space at large scales. The central hypothesis of this work is that, at macroscopic…
From the principles of quantum cosmologies we can justify the reason for an inverse-square law for the cosmological constant with no conflict with observations. Although this general expression for $\Lambda$ is well known in the literature,…
The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle…
I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that 1) are second-order and 2) follow from a…
Scaling symmetries have previously been examined for classical field theories described by singular Lagrangians; in this article, we apply these results to the first-order formulation of General Relativity. It is shown that the dynamical…
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows us to recover quantum mechanics as mechanics on a non-differentiable (fractal) spacetime. The…
The hypothesis is made that, at large scales where General Relativity may be applied, the empty space is scale invariant. This establishes a relation between the cosmological constant and the scale factor of the scale invariant framework.…
The evolution equation is used as the fundamental equation of field theory, which is described entirely by the geometry of the four-dimensional space. The evolution kernel determines the covariant action of physical fields by the proper…
We reflect on the possibility of having a matter action that is invariant only under transverse diffeomorphisms. This possibility is particularly interesting for the dark sector, where no restrictions arise based on the weak equivalence…
We propose a new action principle to be associated with a noncommutative space $(\Ac ,\Hc ,D)$. The universal formula for the spectral action is $(\psi ,D\psi) + \Trace (\chi (D /$ $\Lb))$ where $\psi$ is a spinor on the Hilbert space,…
In the present paper, we revisit gravitational theories which are invariant under TDiffs -- transverse (volume preserving) diffeomorphisms and global scale transformations. It is known that these theories can be rewritten in an equivalent…
The hypothesis of the scale invariance of the macroscopic empty space, which intervenes through the cosmological constant, has led to new cosmological models. They show an accelerated cosmic expansion and satisfy several major cosmological…
The application of the theory of scale relativity to microphysics aims at recovering quantum mechanics as a new non-classical mechanics on a non-derivable space-time. This program was already achieved as regards the Schr\"odinger and Klein…
We study a gravitational model in which scale transformations play the key role in obtaining dynamical $G$ and $\Lambda$. We take a scale non-invariant gravitational action with a cosmological constant and a gravitational coupling constant.…
We generalize the scale invariant gravity by allowing a negative kinetic energy term for the classical scalar field. This gives birth to a new scalar-tensor theory of gravity, in which the scalar field is in fact an auxiliary field. For a…