8 citations · 69 across the 21 of their papers we have counts for
22 papers
A two-point approach to the inverse problem in information geometry
Florio M. Ciaglia, Giuseppe Marmo, Marco Pacelli +2
We formulate the inverse problem in information geometry within a two-point tensorial framework and solve it for general metric-affine manifolds, without imposing any curvature or…
Potential functions in information geometry via bi-forms
Florio M. Ciaglia, Giuseppe Marmo, Marco Pacelli +2
In this paper we develop a general framework for potentials on Lauritzen manifolds, namely smooth manifolds equipped with a pseudo-Riemannian metric and a pair of conjugate affine…
Bi-forms Approach to Potential Functions in Information Geometry
Florio M. Ciaglia, Giuseppe Marmo, Marco Pacelli +2
Contrast functions play a fundamental role in information geometry, providing a means for generating the geometric structures of a statistical manifold: a pseudo-Riemannian metric…
"Fields" in classical and quantum field theories
Alberto Ibort, Arnau Mas, Luca Schiavone
The challenges posed by the development of field theories, both classical and quantum, force us to question their most basic and foundational ideas like the role and origin of spac…
A groupoidal description of elementary particles
Alberto Ibort, Giuseppe Marmo, Arnau Mas +1
In this work, we show that extending the standard description of space-time symmetries from groups of isometries to the more flexible framework of kinematical groupoids allows for…
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…
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…
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…
Symmetries and Reduction. Part II - Lagrangian and Hamilton-Jacobi picture
giuseppe marmo, luca schiavone, alessandro zampini
Following the analysis we have presented in a previous paper (that we refer to as [I]), we describe a Noether theorem related to symmetries, with the associated reduction procedure…
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…
Symmetries and Reduction -- part I -- Poisson and symplectic picture
Giuseppe Marmo, Luca Schiavone, Alessandro Zampini
Coherently with the principle of analogy suggested by Dirac, we describe a general setting for reducing a classical dynamics, and the role of the Noether theorem -- connecting symm…
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…
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…
From Classical Trajectories to Quantum Commutation Relations
Florio M. Ciaglia, Giuseppe Marmo, Luca Schiavone
In describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such different…
Nonlinear Dynamics from Linear Quantum Evolutions
Florio M. Ciaglia, Fabio Di Cosmo, Armando Figueroa +5
Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be…