Related papers: Scale Invariance, Conformality, and Generalized Fr…
We present two examples of non-trivial field theories which are scale invariant, but not conformally invariant. This is done by placing certain field theories, which are conformally invariant in flat space, onto curved backgrounds of a…
The requirements of conformal invariance for two and three point functions for general dimension $d$ on flat space are investigated. A compact group theoretic construction of the three point function for arbitrary spin fields is presented…
Paying attention to conformal invariance as the invariance under local transformations of units of measure, we take a conformal invariant quantum field as a quantum matter theory in which one has the freedom to choose the values of units of…
With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions.…
Implications of noncommutative field theories with commutator of the coordinates of the form $[x^{\mu},x^{\nu}]=i \Lambda_{\quad \omega}^{\mu \nu}x^{\omega}$with nilpotent structure constants are investigated. It is shown that a free…
We expect quantum field theories for matter to acquire intricate corrections due to their coupling to quantum fluctuations of the gravitational field. This can be precisely worked out in 3d quantum gravity: after integrating out quantum…
It is well known that a local, unitary Poincare-invariant 2D QFT with a global scaling symmetry and a discrete non-negative spectrum of scaling dimensions necessarily has both a left and a right local conformal symmetry. In this paper we…
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…
The new manifestation of conformal invariance for a massless scalar particle in a Riemannian spacetime of general relativity is found. Conformal transformations conserve the Hamiltonian and wave function in the Foldy-Wouthuysen…
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…
It was argued recently that conformal invariance in flat spacetime implies Weyl invariance in a general curved background for unitary theories and possible anomalies in the Weyl variation of scalar operators are identified. We argue that…
We demonstrate that there are no scale-invariant one-loop corrections to the superhorizon tensor perturbations from small-scale (potentially enhanced) scalar perturbations, irrespective of the details of inflationary background time…
The idea that local Lorentz invariance might be violated due to new physics that goes beyond the Standard Model of particle physics and Einstein's General Relativity has received a great deal of interest in recent years. At the same time,…
We generalise Einstein's formulation of the traceless Einstein equations to $f(R)$ gravity theories. In the case of the vacuum traceless Einstein equations, we show that a non-constant Weyl tensor leads via a conformal transformation to a…
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…
The role of Lorentz symmetry in noncommutative field theory is considered. Any realistic noncommutative theory is found to be physically equivalent to a subset of a general Lorentz-violating standard-model extension involving ordinary…
A fundamental spacetime scale in the universe leads to noncommutative spacetime and thence to a modified energy - momentum dispersion relation or equivalently to a modification of Lorentz symmetry as shown by the author and others. This…
General Relativity receives quantum corrections relevant at cosmological distance scales from the conformal scalar degrees of freedom required by the trace anomaly of the quantum stress tensor in curved space. In the theory including the…
In the framework of the scale invariant model of the Two Measures Field Theory (TMT), we study the dilaton-gravity sector in the context of spatially flat FRW cosmology. The scale invariance is spontaneously broken due to the intrinsic…
In this work, we formulate a generalized uncertainty principle with both position and momentum operators modified from their canonical forms. We study whether Lorentz symmetry is violated and whether it can be saved with these…