arXiv subjects

Guillermo Capobianco

Publications and source records attributed to Guillermo Capobianco.

3 recordsLinked to original sources

arXiv2026

Data-Based Dynamical Systems Reconstruction: An Adequacy/Reliability Test

In this work, we address the problem of validating the reconstruction of a stochastic system from noisy data. We demonstrate the limitations of criteria based solely on the loss function or on standard metrics used for reconstructing deterministic dynamics. We also propose an exploratory approach, based on a two-step test, which allows for a general assessment of the reconstruction without relying on arbitrary error-tolerance thresholds. However, we discuss how system degeneracy and non-identifiability, together with features intrinsic to stochastic dynamics, impose certain constraints on the application of this test.

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arXiv2019

Holomorphic Path Integrals in Tangent Space for Flat Manifolds

In this paper we study the quantum evolution in a flat Riemannian manifold. The holomorphic functions are defined on the cotangent bundle of this manifold. We construct Hilbert spaces of holomorphic functions in which the scalar product is defined using the exponential map. The quantum evolution is proposed by means of an infinitesimal propagator and the holomorphic Feynman integral is developed via the exponential map. The integration corresponding to each step of the Feynman integral is performed in the tangent space. Moreover, in the case of $S^1$, the method proposed in this paper naturally takes into account paths that must be included in the development of the corresponding Feynman integral.

math-ph↗

arXiv2015

Path Integrals on Euclidean Space Forms

In this paper we develop a quantization method for flat compact manifolds based on path integrals. In this method the Hilbert space of holomorphic functions in the complexification of the manifold is used. This space is a reproducing kernel Hilbert space. A definition of the Feynman propagator, based on the reproducing property of this space, is proposed. In the $\mathbb{R}^n$ case the obtained results coincide with the known expressions.

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