Related papers: Action Principle for Scale Invariance and Applicat…
Starting with a simple two scalar field system coupled to a modified measure that is independent of the metric, we, first, find a Born-Infeld dynamics sector of the theory for a scalar field and second, show that the initial scale…
We develop an action principle to construct the dynamics that give rise to a minimal generalization of Einstein's equations, where the speed of light ($c$), the gravitational constant ($G$) and the cosmological constant ($\Lambda$) are…
A universal formula for an action associated with a noncommutative geometry, defined by a spectal triple $(\Ac ,\Hc ,D)$, is proposed. It is based on the spectrum of the Dirac operator and is a geometric invariant. The new symmetry…
The action principle is used to derive, by an entirely algebraic approach, gauge transformations of the full vacuum-to-vacuum transition amplitude (generating functional) from the Coulomb gauge to arbitrary covariant gauges and in turn to…
Scale invariance has received very little attention in physics. Nevertheless, it provides a natural conceptual foundation for a relational understanding of the universe, where absolute size loses meaning and only dimensionless ratios retain…
The open relativistic two-body problem, when two interacting particles also are in external potentials, is considered in terms of the principle of the least action. Based on the consistent modification of the relativistic version Newton's…
Using our mathematical framework developed in \cite{cresson-pierret_scale} called \emph{scale dynamics}, we propose in this paper a new way of interpreting the problem of adding or modifying potentials in mechanics and specifically in…
Our main interest here is to analyze the gauge invariance issue concerning the noncommutative relativistic particle. Since the analysis of the constraint set from Dirac's point of view classifies it as a second-class system, it is not a…
A new class of gravity-matter model defined with an independent non-Riemannian volume form is studied, in the second order formalism. The action has a global scale invariance symmetry, which can be broken by the equation of motion of the…
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows to recover quantum mechanics as mechanics on a non-differentiable (fractal) space-time. The…
We provide a complete classification of Poincar\'e-invariant scalar field theories with an enlarged set of classical symmetries to leading order in derivatives, namely for the so-called $P(X,\phi)$ theories, in two or more spacetime…
As a spacetime with compact spatial sections, de Sitter spacetime does not have a de Sitter-invariant ground state for a minimally-coupled massless scalar field that gives definite expectation values for any observables not invariant under…
We highlight the fact that the lack of scale invariance in the gravitational field equations of General Relativity results from the underlying assumption that the appropriate scale for the gravitational force should be linked to the atomic…
We propose a 3 + 1 dimensional model of gravity which results in inflation at early times, followed by radiation- and matter-dominated epochs and a subsequent acceleration at late times. Both the inflation and late time acceleration are…
A logic of reciprocity between inertial frames in relative uniform motion is investigated. Relativity allows any reference frame to apply Lorentz Transformation while reciprocity would require the relative frame to use Inverse…
In a recent paper [1], it has been shown that negative norm states are indispensable for a fully covariant quantization of the minimally coupled scalar field in de Sitter space. Their presence, while leaving unchanged the physical content…
We show that scale invariance provides a solution to the fine tuning problem of the cosmological constant. We construct a generalization of the standard model of particle physics which displays exact quantum scale invariance. The matter…
We consider the standard model with local scale invariance. The theory shows exact scale invariance of dimensionally regulated action. We show that massless gauge fields, which may be abelian or non-abelian, lead to vanishing contribution…
In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be…
We generalize the standard model of particle physics such it displays global scale invariance. The gravitational action is also suitably modified such that it respects this symmetry. This model is interesting since the cosmological constant…