Related papers: A generalized Weyl structure with arbitrary non-me…
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical…
A new 8-dimensional conformal gauging avoids the unphysical size change, third order gravitational field equations, and auxiliary fields that prevent taking the conformal group as a fundamental symmetry. We give the structure equations,…
Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl…
In this paper, we present some new results on non-Riemannian geometry, more specifically, asymmetric connections and Weyl's geometry. For asymmetric connections, we show that a projective change in the symmetric part generates a vector…
On a (pseudo-) Riemannian manifold of dimension n > 2, the space of tensors which transform covariantly under Weyl rescalings of the metric is built. This construction is related to a Weyl-covariant operator D whose commutator [D,D] gives…
We investigate the possibility that the observed behavior of test particles outside galaxies, which is usually explained by assuming the existence of dark matter, is the result of the dynamical evolution of particles in a Weyl type…
A Weyl group W is a union of strata (certain subsets which are unions of conjugacy classes) which are the nonempty fibres of a map from W to the set of irreducible representations of W. We give an explicit description of strata in terms of…
We suggest that in the proper definition, Quantum Field Theories are quantum mechanical system which 'live' on the space of causal structures ${\cal C}$ of spacetime. That is, for any QFT a Hilbert space ${\cal H}$ on which local operators…
We classify the possible local holonomy groups of Weyl connections. The Berger-Simons theorem and the Merkulov-Schwachh\"ofer classification of holonomy groups of irreducible torsion-free connections leaves us with the remaining case, where…
A projective structure is Weyl metrizable if it has a representative that preserves a conformal structure. We interpret Weyl metrizability of 3-dimensional projective structures as certain 5-dimensional nondegenerate CR submanifolds in a…
We consider a simple but generic model of gravity where Weyl--invariance is realized thanks to the presence of a gauge field for dilatations. We quantize the theory by suitably defining renormalization group flows that describe the…
Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that "asymmetries cancel". Here we…
We argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions $d \leq 10$. We also study possible curvature corrections to the Weyl…
We define Weyl functors, global modules for equivariant map Lie superalgebras $(\g \otimes A)^{\Gamma}$, where $\g$ is basic classical $\mathbb{C}$- Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}$-algebra. Under…
We present a new formulation for the canonical approach to conformal (Weyl-squared) gravity and its extension by the Einstein-Hilbert term and a nonminimally coupled scalar field. For this purpose we use a unimodular decomposition of the…
We present a construction method for mappings between generalized connections, comprising, e.g., the action of gauge transformations, diffeomorphisms and Weyl transformations. Moreover, criteria for continuity and measure preservation are…
We provide a gauge-invariant theory of gravitation in the context of Weyl Integrable Space-Times. After making a brief review of the theory's postulates, we carefully define the observers' proper-time and point out its relation with…
We define a Weyl-type curvature tensor of $(1,2)$-type to provide a characterization for Finsler metrics of constant flag curvature. This Weyl-type curvature tensor is projective invariant only to projective factors that are Hamel…
We consider the construction of gauge theories of gravity that are invariant under local conformal transformations. We first clarify the geometric nature of global conformal transformations, in both their infinitesimal and finite forms, and…
The Weyl geometry promises potential applications in gravity and quantum mechanics. We study the relationships between the Weyl geometry, quantum entropy and quantum entanglement based on the Weyl geometry endowing the Euclidean metric. We…