arXiv subjects

Manuel Tecchiolli

Publications and source records attributed to Manuel Tecchiolli.

6 recordsLinked to original sources

arXiv2026

The reduced Dirac structure of General Relativity on manifolds with corners

In this paper, the corner Poisson structure of four-dimensional Palatini-Cartan gravity is derived. Building on the classical description of gravity on manifolds with boundary, specifically on the boundary constraint algebra, a pre-Dirac structure on the space of corner fields is obtained together with a reduction procedure that yields a maximal Dirac structure, identified as the graph of a Poisson bivector field, on the reduced space of corner fields. It is further shown that this Poisson structure admits an equivalent affine Poisson description, which naturally exhibits the reduced corner theory as a $BF$-like theory and leads to a BF$^2$V formulation. This provides the basis for a unified framework for the bulk, boundary, and corner structures of Palatini-Cartan gravity.

math-ph↗

arXiv2025

Gravity Coupled with Scalar, SU$(n)$, and Spinor Fields on Manifolds with Null-Boundary

In this paper, we present a theory for gravity coupled with scalar, SU$(n)$ and spinor fields on manifolds with null-boundary. We perform the symplectic reduction of the space of boundary fields and give the constraints of the theory in terms of local functionals of boundary vielbein and connection. For the three different couplings, the analysis of the constraint algebra shows that the set of constraints does not form a first class system.

math-ph↗

arXiv2023

On the Mathematics of Coframe Formalism and Einstein-Cartan Theory -- A Brief Review

This article is a review of what could be considered the basic mathematics of Einstein-Cartan theory. We discuss the formalism of principal bundles, principal connections, curvature forms, gauge fields, torsion form, and Bianchi identities, and eventually, we will end up with Einstein-Cartan-Sciama-Kibble field equations and conservation laws in their implicit formulation.

math-ph↗

arXiv2023

Boundary structure of the standard model coupled to gravity

In this article a description of the reduced phase space of the standard model coupled to gravity is given. For space or time-like boundaries this is achieved as the reduction of a symplectic space with respect to a coisotropic submanifold and with the BFV formalism. For light-like boundaries the reduced phase space is described as the reduction of a symplectic manifold with respect to a set of constraints. Some results about the Poisson brackets of sums of functionals are also proved.

math-ph↗

arXiv2021

Gravitational Constraints on a Lightlike boundary

We analyse the boundary structure of General Relativity in the coframe formalism in the case of a lightlike boundary, i.e., when the restriction of the induced Lorentzian metric to the boundary is degenerate. We describe the associated reduced phase space in terms of constraints on the symplectic space of boundary fields. We explicitly compute the Poisson brackets of the constraints and identify the first- and second-class ones. In particular, in the 3+1 dimensional case, we show that the reduced phase space has two local degrees of freedom, instead of the usual four in the non-degenerate case.

math-ph↗

arXiv2019

Restrictions on torsion-spinor field theory

Torsion propagation and torsion-spin coupling are studied in the perspective of the Velo-Zwanziger method of analysis; specifically, we write the most extensive dynamics of the torsion tensor and the most exhaustive coupling that is permitted between torsion and spinors, and check the compatibility with constraints and hyperbolicity and causality of field equations: we find that some components of torsion and many terms of the torsion-spin interaction will be restricted away and as a consequence we will present the most general theory that is compatible with all restrictions.

physics.gen-ph↗