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Giovanni Canepa

Publications and source records attributed to Giovanni Canepa.

13 recordsLinked to original sources
arXiv2026

Corner Quantization of 4D $BF$ Theory

This note studies the quantized corner structure of four-dimensional $BF$ theory, classifies the associated free and physical corner algebras and constructs possible representations. In the abelian case, for arbitrary closed oriented surfaces and in the presence or absence of a cosmological term, explicit presentations of the corner algebras are obtained in terms of generators and relations, identifying them as infinite-dimensional oscillator-type Lie algebras with an abelian summand. A construction of infinite families of simple modules via bosonic Fock space representations is provided. In the non-abelian case on the torus, the corner algebras are described as quotients constructed from the central extensions of double-loop algebras over certain non-semisimple Lie algebras. A construction of infinite families of simple Fock-type modules of the free corner algebra via an induced module procedure is also provided. The resulting modules descend only trivially to the physical quotient, revealing an obstruction in the present construction in the non-abelian setting.

math-ph↗
arXiv2025

BV Pushforward of Palatini-Cartan gravity

The goal of this note is to show that the standard BV formulation of gravity in the Palatini-Cartan formalism is equivalent, using a BV pushforward, to an AKSZ-like version compatible with BFV data on the boundary.

math-ph↗
arXiv2025

4D Palatini-Cartan Gravity in Hamiltonian Form

In this note the Hamiltonian formulation of four-dimensional gravity, in the Palatini-Cartan formalism, is recovered by elimination of an auxiliary field appearing as part of the connection.

gr-qc↗
arXiv2024

Double BFV quantisation of 3d Gravity

We extend the cohomological setting developed by Batalin, Fradkin and Vilkovisky (BFV), which produces a resolution of coisotropic reduction in terms of hamiltonian dg manifolds, to the case of nested coisotropic embeddings $C\hookrightarrow C_\circ \hookrightarrow F$ inside a symplectic manifold $F$. To this, we naturally assign $\underline{C}$ and $\underline{C_\circ}$, as well as the respective BFV dg manifolds. We show that the data of a nested coisotropic embedding defines a natural graded coisotropic embedding inside the BFV dg manifold assigned to $\underline{C}$, whose reduction can further be resolved using the BFV prescription. We call this construction \emph{double BFV resolution}, and we use it to prove that "resolution commutes with reduction" for a general class of nested coisotropic embeddings. We then deduce a quantisation of $\underline{C}$, from the (graded) geometric quantisation of the double BFV Hamiltonian dg manifold (when it exists), following the quantum BFV prescription. As an application, we provide a well defined candidate space of (physical) quantum states of three-dimensional Einstein--Hilbert theory, which is thought of as a partial reduction of the Palatini--Cartan model for gravity.

math-ph↗
arXiv2024

On the properties of coframes

We consider injectivity and surjectivity of some maps on the exterior algebra of isomorphic finite-dimensional vector spaces. We prove the properties of the maps in full generality, for any dimension of the vector space and any subspace. We also draw a connection with the Palatini-Cartan formulation of General Relativity, for which these maps are of crucial importance.

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↗
arXiv2022

Boundary structure of gauge and matter fields coupled to gravity

The boundary structure of $3+1$-dimensional gravity (in the Palatini-Cartan formalism) coupled to to gauge (Yang-Mills) and matter (scalar and spinorial) fields is described through the use of the Kijowski-Tulczijew construction. In particular, the reduced phase space is obtained as the reduction of a symplectic space by some first class constraints and a cohomological description (BFV) of it is presented.

math-ph↗
arXiv2022

Corner Structure of Four-Dimensional General Relativity in the Coframe Formalism

This note describes a local Poisson structure (up to homotopy) associated to corners in four-dimensional gravity in the coframe (Palatini--Cartan) formalism. This is achieved through the use of the BFV formalism. The corner structure contains in particular an Atiyah algebroid that couples the internal symmetries to diffeomorphisms. The relation with $BF$ theory is also described.

math-ph↗
arXiv2021

General Relativity and the AKSZ construction

In this note the AKSZ construction is applied to the BFV description of the reduced phase space of the Einstein-Hilbert and of the Palatini--Cartan theories in every space-time dimension greater than two. In the former case one obtains a BV theory for the first-order formulation of Einstein--Hilbert theory, in the latter a BV theory for Palatini--Cartan theory with a partial implementation of the torsion-free condition already on the space of fields. All theories described here are BV versions of the same classical system on cylinders. The AKSZ implementations we present have the advantage of yielding a compatible BV-BFV description, which is the required starting point for a quantization in presence of a boundary.

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↗
arXiv2021

Boundary structure of General Relativity in tetrad variables

An explicit, geometric description of the first-class constraints and their Poisson brackets for gravity in the Palatini-Cartan formalism (in space-time dimension greater than three) is given. The corresponding Batalin- Fradkin-Vilkovisky (BFV) formulation is also developed.

math-ph↗
arXiv2018

IDEAL characterization of isometry classes of FLRW and inflationary spacetimes

In general relativity, an IDEAL (Intrinsic, Deductive, Explicit, ALgorithmic) characterization of a reference spacetime metric $g_0$ consists of a set of tensorial equations $T[g]=0$, constructed covariantly out of the metric $g$, its Riemann curvature and their derivatives, that are satisfied if and only if $g$ is locally isometric to the reference spacetime metric $g_0$. The same notion can be extended to also include scalar or tensor fields, where the equations $T[g,ϕ]=0$ are allowed to also depend on the extra fields $ϕ$. We give the first IDEAL characterization of cosmological FLRW spacetimes, with and without a dynamical scalar (inflaton) field. We restrict our attention to what we call regular geometries, which uniformly satisfy certain identities or inequalities. They roughly split into the following natural special cases: constant curvature spacetime, Einstein static universe, and flat or curved spatial slices. We also briefly comment on how the solution of this problem has implications, in general relativity and inflation theory, for the construction of local gauge invariant observables for linear cosmological perturbations and for stability analysis.

gr-qc↗