Related papers: Scale- versus Conformal Invariance Revisited
Implications are explored of promoting non-conformal scale-invariant theories to conformal theories by nonlinearly realizing the missing symmetry. Properties of the associated Nambu-Goldstone mode imply that conformal invariance cannot be…
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…
Statistical systems displaying a strongly anisotropic or dynamical scaling behaviour are characterized by an anisotropy exponent theta or a dynamical exponent z. For a given value of theta, we construct local scale transformations which can…
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…
The most general lagrangian describing spin 2 particles in flat spacetime and containing operators up to (mass) dimension 6 is carefully analyzed, determining the precise conditions for it to be invariant under linearized (transverse)…
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…
Here we follow the mainstream of thinking about physical equivalence of different representations of a theory, regarded as the consequence of invariance of the laws of physics -- represented by an action principle and the derived motion…
We examine the local conformal invariance (Weyl invariance) in tensor-scalar theories used in recently proposed conformal cosmological models. We show that the Noether currents associated with Weyl invariance in these theories vanish. We…
There has been recent interest in the question of whether four dimensional scale invariant unitary quantum field theories are actually conformally invariant. In this note we present a complete analysis of possible scale anomalies in…
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…
Recent studies of scattering amplitudes in planar N=4 SYM theory revealed the existence of a hidden dual superconformal symmetry. Together with the conventional superconformal symmetry it gives rise to powerful restrictions on the planar…
The possibility that global discrete dilation invariance is a fundamental symmetry principle of nature is explored. If the discrete self-similarity observed in nature is exact, then the Principle of General Covariance needs to be broadened…
We extend our program, of coupling theories to scale in order to make their Weyl invariance manifest, to include interacting theories, fermions and supersymmetric theories. The results produce mass terms coinciding with the standard ones…
In this paper a hidden extra symmetry of conformally invariant Lagrangians occuring in physics is pointed out. This symmetry is most apparent in a metric independent, i.e. in a Palatini-like presentation of the variational problem. In such…
We analyze the existence of a dilaton in gauge theories with approximate infrared conformal symmetry. To the extent that these theories are governed in the infrared by an approximate fixed point (walking), the explicit breaking of the…
A gapped ground state of a quantum spin system has a natural length scale set by the gap. This length scale governs the decay of correlations. A common intuition is that this length scale also controls the spatial relaxation towards the…
The aim of the present article is to give physical meaning to the ingredients of standard gauge field theory in the framework of the scale relativity theory. Owing to the principle of the relativity of scales, the scale-space is not…
Scale invariance (SI) can in principle be realized in the elastic response of solid materials. There are two basic options: that SI is a manifest symmetry or that it is spontaneously broken. The manifest case corresponds physically to the…
An argument is made to show that the singularity in the General Theory of Relativity (GTR) is the expression of a non-Machian feature. It can be avoided with a scale-invariant dynamical theory, a property lacking in GTR. It is further…
The relationship between local Weyl scaling invariant models and local dilatation invariant actions is critically scrutinized. While actions invariant under local Weyl scalings can be constructed in a straightforward manner, actions…