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Conformal Gauge Theories, Cartan Geometry and Transitive Lie Algebroids
Our current knowledge about Universe rests on the existence of four fundamental interactions. These are : gravitation, electromagnetism, weak interaction and strong interaction. They have formed the conceptual basis of modern physics since half a century.
The Dressing Field Method of Gauge Symmetry Reduction, a Review with Examples
Gauge symmetries are a cornerstone of modern physics but they come with technical difficulties when it comes to quantization, to accurately describe particles phenomenology or to extract observables in general. These shortcomings must be met by essentially finding a way to effectively reduce gauge symmetries.
Tractors and Twistors from conformal Cartan geometry: a gauge theoretic approach, I. Tractors
Tractors and Twistors bundles both provide natural conformally
covariant calculi on 4D-Riemannian manifolds. They have different
origins but are closely related, and usually constructed bottom-up
from prolongation of defining differential equations.
Tractors and twistors from conformal Cartan geometry: a gauge theoretic approach II. Twistors
Our current knowledge about Universe rests on the existence of four fundamental interactions. These are : gravitation, electromagnetism, weak interaction and strong interaction. They have formed the conceptual basis of modern physics since half a century.
A note on Weyl invariance in gravity and the Wess–Zumino functional
It is shown that the explicit calculation of the Wess–Zumino functional pertaining to the breaking term of the Weyl symmetry for the Einstein–Hilbert action allows to restore the Weyl symmetry by introducing the extra dilaton field as Goldstone field. Adding the Wess–Zumino counter-term to the Einstein–Hilbert action reproduces the usual Weyl invariant action used in standard literature
Weyl Gravity and Cartan Geometry:
We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned with two theories: the first one is the associated Yang-Mills-like Lagrangian, while the second, inspired by [1], is a slightly more general one that relaxes the conformal Cartan geometry.
The scientific demarcation problem: a formal and model-based approach to falsificationism
The problem of demarcating between what is scientific and what is pseudoscientific or merely unscientific – in other words, the problem of defining scientificity – remains open. The modern debate was firstly structured around Karl Popper’s falsificationist epistemology from the 1930’s, before diversifying a few decades later.