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.
General Relativity and the AKSZ Construction Canepa, G.; Cattaneo, A. S.; Schiavina, M.
Communications in mathematical physics,
2021/8, Letnik:
385, Številka:
3
Journal Article
Recenzirano
Odprti dostop
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.
Within a geometrical context, we derive an explicit formula for the computation of the symmetric logarithmic derivative for arbitrarily mixed quantum systems, provided that the structure constants of ...the associated unitary Lie algebra are known. To give examples of this procedure, we first recover the known formulae for two-level mixed and three-level pure state systems and then apply it to the novel case of U(3), that is for arbitrarily mixed three-level systems (q-trits). Exploiting the latter result, we finally calculate an expression for the Fisher tensor for a q-trit considering also all possible degenerate subcases.
•Formula for the symmetric logarithmic derivative, based on the Lie algebra structure.•Reformulate known results, clarifying and solving ambiguities in previous definitions.•For non-degenerate states of dimension 2, 3 the SLD is uniquely defined.•Compute the SLD for a q-trit with degenerations and associated Fisher tensor.
The triadic description of general relativity in three dimensions is known to be a BF theory. Diffeomorphisms, as symmetries, are easily recovered on-shell from the symmetries of BF theory. This note ...describes an explicit off-shell BV symplectomorphism between the BV versions of the two theories, each endowed with their natural symmetries.
Geo-information on settlements from Earth Observation offers a base for objective and scalable monitoring of the evolution of cities and settlements, including their location, extent and other ...attributes. In this work, we deploy the best available global knowledge on the presence of human settlements and built-up structures derived from Earth Observation to advance the understanding of the human presence on Earth. We start from a concept of Generalised Settlement Area to identify the Earth surface within which any built-up structure is present. We further characterise the resulted map by using an agreement map among the state of the art of remote sensing products mapping built-up areas or other strictly related semantic abstractions as urban areas or artificial surfaces. The agreement map is formed by a grid of 1 km
2
, where each cell is classified according to the number of EO-derived products reporting any positive occurrence of the abstractions related to the presence of built-up structures. The paper describes the characteristics of the Generalised Settlement Area, the differences in the agreement map across geographic regions of the world, and outlines the implications for potential users of the EO-derived products used in this study.
BV equivalence with boundary Simão, F. M. Castela; Cattaneo, A. S.; Schiavina, M.
Letters in mathematical physics,
2023/2, Letnik:
113, Številka:
1
Journal Article
Recenzirano
Odprti dostop
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.
Investigating the interactions between the physical environment and early life history is crucial to understand the mechanisms that shape the genetic structure of marine populations. Here, we ...assessed the genetic differentiation in a species with larval dispersal, the Mediterranean shore crab (Carcinus aestuarii) in the Adriatic Sea (central Mediterranean), and we investigated the role of oceanic circulation in shaping population structure. To this end, we screened 11 polymorphic microsatellite loci from 431 individuals collected at eight different sites. We found a weak, yet significant, genetic structure into three major clusters: a northern Adriatic group, a central Adriatic group and one group including samples from southern Adriatic and Ionian seas. Genetic analyses were compared, under a seascape genetics approach, with estimates of potential larval connectivity obtained with a coupled physical–biological model that integrates a water circulation model and a description of biological traits affecting dispersal. The cross‐validation of the results of the two approaches supported the view that genetic differentiation reflects an oceanographic subdivision of the Adriatic Sea into three subbasins, with circulation patterns allowing the exchange of larvae through permanent connections linking north Adriatic sites and ephemeral connections like those linking the central Adriatic with northern and southern locations.
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