From classical to quantum models: the regularising role of integrals, symmetry and probabilities

In physics, when a mathematical model becomes really inoperative  in regard with correct predictions, one is forced to replace it with a new one. It is precisely what happened with the emergence of quantum physics. Classical models were (progressively) superseded by quantum ones through quantization prescriptions.  These procedures appear often as ad hoc recipes. I will describe  well defined quantizations,  based on integral calculus and  Weyl-Heisenberg symmetry. They are described in simple terms through one of the most basic examples of mechanics.

Dark energy and fundamental physics: the landscape, the swampland, and all that

While theoretical efforts continue to explore possible explanations for the late-time cosmic acceleration, as well as the problem of the cosmological constant, we expect future cosmological surveys to judge against or for many of the proposed theories. In this talk, I will first review the status of models of dark energy provided by fundamental physics (supergravity and string theory) by presenting, as an example, a recently discovered class of $\alpha$-attractor models of quintessential inflation which combine dark energy and inflation in a unified framework.

Teleparallel gravity (TEGR) as a gauge theory: Translation or Cartan connection?

We question the status of TEGR, the Teleparallel Equivalent of General Relativity,
as a gauge theory of translations. We observe that TEGR (in its usual translation-gauge view) does not seem to realize the generally admitted requirements for a gauge theory for some symmetry group G: namely it does not present
a mathematical structure underlying the theory which relates to a principal G-bundle and the choice of a connection on it (the gauge field). We point out that, while it is usually presented as absent, the gauging of the


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