28 citations · 247 across the 36 of their papers we have counts for
37 papers
Towards a category-theoretic foundation of Classical and Quantum Information Geometry
Florio M. Ciaglia, Fabio Di Cosmo, Laura González-Bravo
We introduce the category , whose objects are pairs of W-algebras and normal states and whose morphisms are state-preserving unital completely positive (CPU) m…
The Geometry of the solution space of first order Hamiltonian field theories III: Palatini's formulation of General Relativity
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +3
We complete the program started in two companion papers of defining a Poisson bracket structure on the space of solutions of the equations of motion of first order Hamiltonian fiel…
On the categorical foundations of quantum information theory: Categories and the Cramer-Rao inequality
Florio M. Ciaglia, Fabio Di Cosmo, Laura González-Bravo +2
An extension of Cencov's categorical description of classical inference theory to the domain of quantum systems is presented. It provides a novel categorical foundation to the theo…
Some remarks on the notion of transitions
Florio M. Ciaglia aand Fabio Di Cosmo
In this paper some reflections on the concept of transition are presented: groupoids are introduced as models for the construction of a ``generalized logic'' whose basic statements…
Can Čencov meet Petz?
Florio M. Ciaglia, Fabio Di Cosmo, Laura González-Bravo
We discuss how to exploit the recent formulation of classical and quantum information geometry in terms of normal states on -algebras to formulate a problem that unifies Cen…
Groupoid and algebra of the infinite quantum spin chain
Florio Maria Ciaglia, Fabio Di Cosmo, Paolo Facchi +3
It is well known that certain features of a quantum theory cannot be described in the standard picture on a Hilbert space. In particular, this happens when we try to formally frame…
The Geometry of the solution space of first order Hamiltonian field theories II: non-Abelian gauge theories
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +3
We go on with the program started in the companion paper [CDI+] of defining a Poisson bracket structure on the space of solutions of the equations of motion of first order Hamilton…
The Geometry of the solution space of first order Hamiltonian field theories I: from particle dynamics to free Electrodynamics
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +3
We analyse the problem of defining a Poisson bracket structure on the space of solutions of the equations of motions of first order Hamiltonian field theories. The cases of Hamilto…
G-dual teleparallel connections in Information Geometry
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +1
Given a real, finite-dimensional, smooth parallelizable Riemannian manifold endowed with a teleparallel connection determined by a choice of a global bas…
Dynamical maps and symmetroids
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +1
Starting from the canonical symmetroid associated with a groupoid , the issue of describing dynamical maps in the groupoidal approach to Quantum Mechanics is ad…
Quantum Tomography and Schwinger's Picture of Quantum Mechanics
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +1
In this paper the problem of tomographic reconstruction of states is investigated within the so-called Schwinger's picture of Quantum Mechanics in which a groupoid is associated wi…
Monotone metric tensors in Quantum Information Geometry
Florio M. Ciaglia, Fabio Di Cosmo, Fabio Di Nocera +1
We review some geometrical aspects pertaining to the world of monotone quantum metrics in finite dimensions. Particular emphasis is given to an unfolded perspective for quantum sta…
Symmetries and Covariant Poisson brackets on pre-symplectic manifolds
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +3
Noticing that the space of the solutions of a first order Hamiltonian field theory has a pre-symplectic structure, we describe a class of conserved charges on it associated to the…
Feynman's Propagator in Schwinger's picture of Quantum Mechanics
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +3
A novel derivation of Feynman's sum-over-histories construction of the quantum propagator using the groupoidal description of Schwinger picture of Quantum Mechanics is presented. I…
A quantum route to the classical Lagrangian formalism
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +3
Using the recently developed groupoidal description of Schwinger's picture of Quantum Mechanics, a new approach to Dirac's fundamental question on the role of the Lagrangian in Qua…
Schwinger's picture of quantum mechanics: 2-groupoids and symmetries
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +2
Starting from the groupoid approach to Schwinger's picture of Quantum Mechanics, a proposal for the description of symmetries in this framework is advanced.It is shown that, given…
Covariant reduction of classical Hamiltonian Field Theories: From D'Alembert to Klein-Gordon and Schrödinger
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +2
A novel reduction procedure for covariant classical field theories, reflecting the generalized symplectic reduction theory of Hamiltonian systems, is presented. The departure point…
Covariant Variational Evolution and Jacobi Brackets: Fields
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +2
The analysis of the covariant brackets on the space of functions on the solutions to a variational problem in the framework of contact geometry initiated in the companion letter Re…
Covariant Variational Evolution and Jacobi Brackets: Particles
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +2
The formulation of covariant brackets on the space of solutions to a variational problem is analyzed in the framework of contact geometry. It is argued that the Poisson algebra on…
Lagrangian description of Heisenberg and Landau-von Neumann equations of motion
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +3
An explicit Lagrangian description is given for the Heisenberg equation on the algebra of operators of a quantum system, and for the Landau-von Neumann equation on the manifold of…
Schwinger's Picture of Quantum Mechanics IV: Composition and independence
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +1
The groupoids description of Schwinger's picture of quantum mechanics is continued by discussing the closely related notions of composition of systems, subsystems, and their indepe…
Schwinger's picture of Quantum Mechanics
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +1
In this paper we will present tha main features of what can be called Schwinger's foundational approach to Quantum Mechanics. The basic ingredients of this formulation are the \tex…
Geometry from divergence functions and complex structures
Florio M. Ciaglia, Fabio Di Cosmo, Armando Figueroa +2
Motivated by the geometrical structures of quantum mechanics, we introduce an almost-complex structure on the product of any parallelizable statistical manifold …
Evolutionary equations and constraints: Maxwell equations
Florio M. Ciaglia, Fabio Di Cosmo, Giuseppe Marmo +1
By fixing a reference frame in spacetime, it is possible to split the Euler-Lagrange equations associated with a degenerate Lagrangian into purely evolutionary equations and constr…