Michele Schiavina

Last Name

Schiavina

First Name

Michele

ORCID

0000-0001-5760-4794

Show all metadata

Search Results

Publications 1 - 10 of 11

BV analysis of Polyakov and Nambu–Goto theories with boundary
Martinoli, S.; Schiavina, Michele (2022)
Letters in Mathematical Physics
The Batalin–Vilkovisky data for Polyakov string theory on a manifold with (non-null) boundary are shown to induce compatible Batalin–Fradkin–Vilkovisky data, thus allowing BV-quantisation on manifolds with boundary. On the other hand, the analogous formulation of Nambu–Goto string theory fails to satisfy the needed regularity requirements. As a by-product, a concise description is given of the reduced phase spaces of both models and their relation, for any target d-dimensional Lorentzian manifold.
Asymptotic Symmetries in the BV-BFV Formalism
Rejzner, Kasia; Schiavina, Michele (2021)
Communications in Mathematical Physics
We show how to derive asymptotic charges for field theories on manifolds with “asymptotic” boundary, using the BV-BFV formalism. We also prove that the conservation of said charges follows naturally from the vanishing of the BFV boundary action, and show how this construction generalises Noether’s procedure. Using the BV-BFV viewpoint, we resolve the controversy present in the literature, regarding the status of large gauge transformation as symmetries of the asymptotic structure. We show that even though the symplectic structure at the asymptotic boundary is not preserved under these transformations, the failure is governed by the corner data, in agreement with the BV-BFV philosophy. We analyse in detail the case of electrodynamics and the interacting scalar field, for which we present a new type of duality to a sourced two-form model.
General Relativity and the AKSZ Construction
Canepa, Giovanni; Cattaneo, Alberto S.; Schiavina, Michele (2021)
Communications in Mathematical Physics
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.
A Lie–Rinehart algebra in general relativity
Blohmann, Christian; Schiavina, Michele; Weinstein, Alan (2023)
Pure and Applied Mathematics Quarterly
We construct a Lie–Rinehart algebra over an infinitesimal extension of the space of initial value fields for Einstein’s equations. The bracket relations in this algebra are precisely those of the constraints for the initial value problem. The Lie–Rinehart algebra comes from a slight generalization of a Lie algebroid in which the algebra consists of sections of a sheaf rather than a vector bundle. (An actual Lie algebroid had been previously constructed by Blohmann, Fernandes, and Weinstein over a much larger extension.) The construction uses the BV–BFV (Batalin–Fradkin–Vilkovisky) approach to boundary value problems, starting with the Einstein equations themselves, to construct an L∞-algebroid over a graded manifold which extends the initial data. The Lie–Rinehart algebra is then constructed by a change of variables. One of the consequences of the BV–BFV approach is a proof that the coisotropic property of the constraint set follows from the invariance of the Einstein equations under space-time diffeomorphisms.
Boundary structure of general relativity in tetrad variables
Canepa, Giovanni; Cattaneo, Alberto S.; Schiavina, Michele (2021)
Advances in Theoretical and Mathematical Physics
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.
Perturbative BF Theory in Axial, Anosov Gauge
Schiavina, Michele; Stucker, Thomas (2024)
Annales Henri Poincaré
The twisted Ruelle zeta function of a contact, Anosov vector field, is shown to be equal, as a meromorphic function of the complex parameter h ϵ C and up to a phase, to the partition function of an h-linear quadratic perturbation of BF theory, using an “axial” gauge fixing condition given by the Anosov vector field. Equivalently, it is also obtained as the expectation value of the same quadratic, h-linear, perturbation, within a perturbative quantisation scheme for BF theory, suitably generalised to work when propagators have distributional kernels.
Kähler fibrations in quantum information theory
Contreras, Ivan; Schiavina, Michele (2022)
Manuscripta Mathematica
We discuss the fibre bundle of co-adjoint orbits of compact Lie groups, and show how it admits a compatible Kähler structure. The case of the unitary group allows us to reformulate the geometric framework of quantum information theory. In particular, we show that the Fisher information tensor gives rise to a structure that is sufficiently close to a Kähler structure to generalise some classical result on co-adjoint orbits. © 2021 Springer Nature Switzerland AG
Towards Holography in the BV-BFV Setting
Mnev, Pavel; Schiavina, Michele; Wernli, Konstantin (2020)
Annales Henri Poincaré
BV equivalence with boundary
Castela Simão, Francisco M.; Cattaneo, Alberto S.; Schiavina, Michele (2023)
Letters in Mathematical Physics
An extension of the notion of classical equivalence of equivalence in the Batalin–Vilkovisky (BV) and Batalin–Fradkin–Vilkovisky (BFV) frameworks for local Lagrangian field theory on manifolds possibly with boundary is discussed. Equivalence is phrased in both a strict and a lax sense, distinguished by the compatibility between the BV data for a field theory and its boundary BFV data, necessary for quantisation. In this context, the first- and second-order formulations of nonabelian Yang–Mills and of classical mechanics on curved backgrounds, all of which admit a strict BV–BFV description, are shown to be pairwise equivalent as strict BV–BFV theories. This in particular implies that their BV complexes are quasi-isomorphic. Furthermore, Jacobi theory and one-dimensional gravity coupled with scalar matter are compared as classically equivalent reparametrisation-invariant versions of classical mechanics, but such that only the latter admits a strict BV–BFV formulation. They are shown to be equivalent as lax BV–BFV theories and to have isomorphic BV cohomologies. This shows that strict BV–BFV equivalence is a strictly finer notion of equivalence of theories.
Fully extended BV-BFV description of General Relativity in three dimensions
Canepa, Giovanni; Schiavina, Michele (2022)
Advances in Theoretical and Mathematical Physics
We compute the extension of the BV theory for three-dimensional general relativity to all higher-codimension strata -boundaries, corners and vertices -in the BV-BFV framework. Moreover, we show that such extension is strongly equivalent to (nondegenerate) BF theory at all codimensions.

Publications 1 - 10 of 11

Michele Schiavina

Last Name

First Name

ORCID

Organisational unit

Filters

Search Results