arXiv subjects

Lucas T. Cardoso

Publications and source records attributed to Lucas T. Cardoso.

4 recordsLinked to original sources

arXiv2024

sQFT: an autonomous explanation of the interactions of quantum particles

Successful applications of a conceptually novel setup of Quantum Field Theory, that accounts for all subtheories of the Standard Model (QED, Electroweak Interaction and Higgs, Yang-Mills and QCD) and beyond (Helicity 2), call for a perspective view in a broader conceptual context. The setting is "autonomous" in the sense of being intrinsically quantum. Its principles are: Hilbert space, Poincaré symmetry and causality. Its free quantum fields are obtained from Wigner's unitary representations of the Poincaré group, with only physical and observable degrees of freedom. A "quantization" of an "underlying" classical theory is not needed. It allows renormalizable perturbation theory with interactions whose detailed structure, and in some cases even the particle content, is predicted by internal consistency. The results confirm and extend observable predictions for the interactions of the SM without assuming a "principle" of gauge invariance.

hep-th↗

arXiv2022

Is time the real line?

This paper is devoted to discussing the topological structure of the arrow of time. In the literature, it is often accepted that its algebraic and topological structures are that of a one-dimensional Euclidean space $\mathbb{E}^1$, although a critical review on the subject is not easy to be found. Hence, leveraging on an operational approach, we collect evidences to identify it structurally as a normed vector space $(\mathbb{Q}, |\cdot|)$, and take a leap of abstraction to complete it, up to isometries, to the real line. During the development of the paper, the space-time is recognized as a fibration, with the fibers being the sets of simultaneous events. The corresponding topology is also exposed: open sets naturally arise within our construction, showing that the classical space-time is non-Hausdorff. The transition from relativistic to classical regimes is explored too.

gr-qc↗

arXiv2021

Properties of the Digital Root and its Extension to Rational Numbers -- an Algebraic Approach

This paper contains an algebraic constructive and self-contained account of the invariance rule of the digital root under division for an arbitrary natural basis representation. Both the cases of repeating and non-repeating fractionals are treated. In the preliminary section some known results such as the uniqueness in the representation of a fraction are discussed for both the finite and infinite bases cases. Simple examples are introduced throughout the text for illustrative purposes.

math.NT↗

arXiv2017

String chopping and time-ordered products of linear string-localized quantum fields

For a renormalizability proof of perturbative models in the Epstein--Glaser scheme with string-localized quantum fields, one needs to know what freedom one has in the definition of time-ordered products of the interaction Lagrangian. This paper provides a first step in that direction. The basic issue is the presence of an open set of $n$-tuples of strings which cannot be chronologically ordered. We resolve it by showing that almost all such string configurations can be dissected into finitely many pieces which can indeed be chronologically ordered. This fixes the time-ordered products of linear field factors outside a nullset of string configurations. (The extension across the nullset, as well as the definition of time-ordered products of Wick monomials, will be discussed elsewhere.)

math-ph↗