Related papers: Scale invariance and constants of motion
A scale-invariant universe can have a period of accelerated expansion at early times: inflation. We use a frame-invariant approach to calculate inflationary observables in a scale invariant theory of gravity involving two scalar fields -…
We consider fluctuations in a perfect irrotational fluid coupled to gravity in an Einstein static universe background. We show that the homogeneous linear perturbations of the scalar and metric fluctuations in the Einstein static universe…
The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell's equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from…
An approximately scale invariant spectrum generating the seeds of structure formation is derived from a bimetric gravity theory. By requiring that the amplitude of the CMB fluctuations from the model matches the observed value, we determine…
A system is invariant with respect to an input transformation if we can transform any dynamic input by this function and obtain the same output dynamics after adjusting the initial conditions appropriately. Often, the set of all such input…
We explore phenomenological consequences of coupling a non-conformal scale-invariant theory to the standard model. We point out that, under certain circumstances, non-conformal scale-invariant theories have oscillating correlation functions…
Force networks form the skeleton of static granular matter. They are the key ingredient to mechanical properties, such as stability, elasticity and sound transmission, which are of utmost importance for civil engineering and industrial…
In this Letter, we address the question of whether the conformal invariance can be considered as a global symmetry of a theory of fundamental interactions. To describe Nature, this theory must contain a mechanism of spontaneous breaking of…
The 3+1 Hamiltonian Einstein equations, reduced by imposing two commuting spacelike Killing vector fields, may be written as the equations of the $SL(2,R)$ principal chiral model with certain `source' terms. Using this formulation, we give…
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…
If scale invariance is a classical symmetry then both the Planck scale and the weak scale should emerge as quantum effects. We show that this can be realized in simple scale invariant theories with a hidden sector. The weak/Planck scale…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
The suspicion that the existence of a minimal uncertainty in position measurements violates Lorentz invariance seems unfounded. It is shown that the existence of such a nonzero minimal uncertainty in position is not only consistent with…
Many self-gravitating systems often show scaling properties in their mass density, system size, velocities and so on. In order to clarify the origin of these scaling properties, we consider the stationary state of N-body system with inverse…
The motion of a charged particle moving on a flat surface is studied through the constants of motion associated to the system, given the magnetic gauge. The usual Landau' solution and the non separable solution for the Landau's gauge are…
A closed mathematical model of the statistical self-gravitating system of scalar charged particles for conformal invariant scalar interactions is constructed on the basis of relativistic kinetics and gravitation theory. Asymptotic…
The suspicion that the existence of a minimal uncertainty in position measurements violates Lorentz invariance seems unfounded. It is shown that the existence of such a nonzero minimal uncertainty in position is not only consistent with…
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,…
Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At…
The linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid universe is reconsidered and formally simplified by introducing new covariant and gauge-invariant variables with physical interpretations on…