Related papers: Scale invariance and constants of motion
The energy density of the universe today may be dominated by the vacuum energy of a slowly rolling scalar field. Making a quantum expansion around such a time dependent solution is found to break fundamental symmetries of quantum field…
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…
We re-consider the quantum mechanics of scale invariant potentials in two dimensions. The breaking of scale invariance by quantum effects is analyzed by the explicit evaluation of the phase shift and the self-adjoint extension method. We…
The use in the action integral of totally divergent densities in generally coordinate invariant theories can lead to interesting mechanisms of spontaneous symmetry breaking of scale invariance. With dependence in the action on a metric…
We develop a formulation of particle mechanics in which the functional relation between force and kinetic energy is derived directly from local conservation mechanical energy $E$, rather than postulated through Newton's second law or a…
Any symmetry reduces a second-order differential equation to a first-order equation: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetries of only the equations of motion…
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…
We compute the cosmological constant in a scale invariant scalar field theory. The gravitational action is also suitably modified to respect scale invariance. Due to scale invariance the theory does not admit a cosmological constant term.…
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…
Scale without conformal symmetry corresponds to an inhomogeneous conservation equation for the virial current sourced by the trace of the energy-momentum tensor. Fluids that are just scale-invariant differ qualitatively from their conformal…
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in…
The incorporation of a small cosmological constant within radiatively-broken scale-invariant models is discussed. We show that phenomenologically consistent scale-invariant models can be constructed which allow a small positive cosmological…
Maxwell equations and the equations of General Relativity are scale invariant in empty space. The presence of charge or currents in electromagnetism or the presence of matter in cosmology are preventing scale invariance. The question arises…
We consider a model for gravity that is invariant under global scale transformations. It includes one extra real scalar field coupled non-minimally to the gravity fields. In this model all the dimensionful parameters like the gravitational…
In this paper we shall show that, unless the affine geometrical structure of the underlying spacetime manifold is specified, there is an ambiguity in the understanding of the scale invariance -- also Weyl invariance -- of the given theory…
Our conventional system of physical units is based on local or microscopic {\it dimensional} quantities which are {\it defined}, for convenience or otherwise aesthetic reasons, to be spacetime-independent. A more general choice of units may…
A simple conservation law formula for field equations with a scaling symmetry is presented. The formula uses adjoint-symmetries of the given field equation and directly generates all local conservation laws for any conserved quantities…
Scale invariance supplemented by the requirement of the absence of new heavy particles may play an important role in addressing the hierarchy problem. We discuss how the Standard Model may become scale invariant at the quantum level above a…
A large value of the cosmological constant (CC) is induced in the Standard Model (SM) of Elementary Particle Physics because of Spontaneous Symmetry Breaking. To provide a small value of the observable CC one has to introduce the vacuum…
We give a non-perturbative proof that any 4D unitary and Lorentz-invariant quantum field theory with a conserved scale current is in fact conformally invariant. We show that any scale invariant theory (unitary or not) must have either a…