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Roberto Casalbuoni

Publications and source records attributed to Roberto Casalbuoni.

At least 19 recordsLinked to original sources
arXiv2026

Massive and massless particles in Mielke--Baekler geometries

The Mielke--Baekler geometries are three-dimensional reductive homogeneous spacetimes together with a choice of invariant connection which is compatible with a lorentzian metric. The spacetimes generalise Minkowski and (anti)de~Sitter spacetimes in that the invariant metric connection can have torsion, a peculiarity of three dimensions. Using coadjoint orbits and the techniques of nonlinear realisations, we construct worldline actions for massive and massless spinning particles moving in these spacetimes. We pay particular attention to the so-called teleparallel branch, in which the curvature of the invariant connection vanishes. Apart from the trivial Minkowski case, this singles out anti-de~Sitter spacetime, as the only of these lorentzian manifolds admitting an invariant Weitzenböck connection; that is, a flat connection with torsion. The introduction of a Wess--Zumino term describing spin has, as a main consequence, the appearance of dynamical sectors (denoted ``regular'' and ``critical''), with a different number of physical degrees of freedom. In particular, in the massive case, we discuss the formulation of the dynamics in terms of either the Weitzenböck or the Levi-Civita connection, and the emergence of a Papapetrou-type forcing term in the critical sector. For the massless particle we study the Noether symmetries of the action, which, for the spinless case, include the conformal transformations. For nonzero spin, only the Killing subset survives as genuine Noether transformations in the regular sector, while in the critical sector any conformal Killing contribution can be set to zero by a gauge transformation.

hep-th↗
arXiv2026

From Florence to Fermions: a historical reconstruction of the origins of Fermi's statistics one hundred years later

Aim of this paper is to retrace the path that led the young Enrico Fermi to write his paper on the statistics of an ideal monatomic gas. This discovery originated in his interest, which he had shown since his formative years, in the absolute entropy constant and in the problems he highlighted in Sommerfeld's quantization in the case of identical particle systems. The fundamental step taken by Fermi in writing his work on statistics was to apply the Exclusion Principle, formulated for electrons in an atom and which could therefore have been a pure effect due to dynamics, to a system of non-interacting particles.

physics.hist-ph↗
arXiv2025

A Celestial Kinematical Interpretation for an Extended BMS$_4$

Motivated by the work of Longhi and Materassi, who constructed a realisation of the (centreless) BMS$_4$ algebra for the massive Klein-Gordon field in $3+1$, we build a realisation of the (centreless) massless BMS$_4$ algebra including super-rotations. This realisation depends only on the momenta in the lightcone expressed in celestial coordinates without any reference to the Klein--Gordon field. The quadratic Casimir of the Lorentz algebra is written in terms of a second order differential operator and the volume form plays an essential role in this construction. The BMS$_4$ algebra in terms of vector fields shows its kinematical nature, like the Poincaré algebra. We also construct a dynamical realisation of BMS$_4$ from the symplectic structure on the solutions of the massless four-dimensional Klein--Gordon field in terms of quadratic expressions of the Fourier modes and plane waves invariant under translations. Using the Mellin transform, we rewrite the Klein--Gordon field in terms of the boost invariant basis, and write down the corresponding BMS$_4$ realization. We also provide the relation with spherical harmonics, linking our results with the solutions of Longhi-Materassi, which are in fact a subset of ours.

hep-th↗
arXiv2024

Non equivalence of Carroll limits in relativistic string theory

We construct new Carroll strings in flat space by considering the Carroll limit of equivalent relativistic string theories at classical level. In the limit these Carroll strings are no longer equivalent and have different degrees of freedom. This fact is due to a general phenomenon that the configuration space and canonical Lagrangians are no longer equivalent after a singular redefinition of the variables and of the parameters of the starting Lagrangians.

hep-th↗
arXiv2023

Superconformal interacting particles

The free massless superparticle is reanalysed, in particular by performing the Gupta-Bleuler quantization, using the first and second class constraints of the model, and obtaining, as a result, the Weyl equation for the spinorial component of the chiral superfield. Then we construct a superconformal model of two interacting massless superparticles from the free case by the introduction of an invariant interaction. The interaction introduces an effective mass for each particle by modifying the structure of fermionic constraints, all becoming second class. The quantization of the model produces a bilocal chiral superfield. We also generalise the model by considering a system of superconformal interacting particles and its continuum limit.

hep-th↗
arXiv2023

Two interacting conformal Carroll particles

In this note we analyse two different models of two interacting conformal Carroll particles that can be obtained as the Carrollian limit of two relativistic conformal particles. The first model describes particles with zero velocity and exhibits infinite dimensional symmetries which are reminiscent of the BMS symmetries. A second model of interaction of Carrollian particles is proposed, where the particles have non zero velocity and therefore, as a consequence of the limit c to 0, are tachyons. Infinite dimensional symmetries are present also in this model.

hep-th↗
arXiv2023

A brief history of Florentine physics from the 1920s to the end of the 1960s

The history of the Institute of Physics at the University of Florence is traced from the beginning of the 20th century, with the arrival of Antonio Garbasso as Director (1913), to the 1960s. Thanks to Garbasso's expertise, not only did the Institute gain new premises on Arcetri hill, where the Astronomical Observatory was already located, but it also formed a brilliant group of young physicists made up of Enrico Fermi, Franco Rasetti, Enrico Persico, Bruno Rossi, Gilberto Bernardini, Daria Bocciarelli, Lorenzo Emo Capodilista, Giuseppe Occhialini and Giulio Racah, who were engaged in the emerging fields of Quantum Mechanics and Cosmic Rays. This Arcetri School disintegrated in the late 1930s for the transfer of its protagonists to chairs in other universities, for the environment created by the fascist regime and, to some extent, for the racial laws. After the war, the legacy was taken up by some students of this school who formed research groups in the field of nuclear physics and elementary particle physics. As far as theoretical physics was concerned, after the Fermi and Persico periods these studies enjoyed a new expansion towards the end of the 1950s, with the arrival of Giacomo Morpurgo and above all, that of Raoul Gatto, who created the first real Italian school of Theoretical Physics at Arcetri.

physics.hist-ph↗
arXiv2021

World-Line Description of Fractons

We formulate the word-line approach of the field theory of fractons and their symmetries. The distinction between the different models is based on their dispersion relations for the energy. In order to study the sub-system symmetries, we construct the Routhians associated with the particle Lagrangians considered. We also construct the pseudoclassical description of spinning fractons.

hep-th↗
arXiv2021

Translational symmetries of quadratic lagrangians

In this paper we show that a quadratic lagrangian, with no constraints, containing ordinary time derivatives up to the order $m$ of $N$ dynamical variables, has $2mN$ symmetries consisting in the translation of the variables with solutions of the equations of motion. We construct explicitly the generators of these transformations and prove that they satisfy the Heisenberg algebra. We also analyse other specific cases which are not included in our previous statement: the Klein-Gordon lagrangian, $N$ Fermi oscillators and the Dirac lagrangian. In the first case, the system is described by an equation involving partial derivatives, the second case is described by Grassmann variables and the third shows both features. Furthermore, the Fermi oscillator and the Dirac field lagrangians lead to second class constraints. We prove that also in these last two cases there are translational symmetries and we construct the algebra of the generators. For the Klein-Gordon case we find a continuum version of the Heisenberg algebra, whereas in the other cases, the Grassmann generators satisfy, after quantization, the algebra of the Fermi creation and annihilation operators.

hep-th↗
arXiv2020

A particle model with extra dimensions from Coadjoint Poincare' Symmetry

Starting from the coadjoint Poincaré algebra we construct a point particle relativistic model with an interpretation in terms of extra-dimensional variables. The starting coadjoint Poincaré algebra is able to induce a mechanism of dimensional reduction between the usual coordinates of the Minkowski space and the extra-dimensional variables which turn out to form an antisymmetric tensor under the Lorentz group. Analysing the dynamics of this model, we find that, in a particular limit, it is possible to integrate out the extra variables and determine their effect on the dynamics of the material point in the usual space time. The model describes a particle in $D$ dimensions subject to a harmonic motion when one of the parameters of the model is negative. The result can be interpreted as a modification to the flat Minkowski metric with non trivial Riemann, Ricci tensors and scalar curvature

hep-th↗
arXiv2019

Non-relativistic $k$-contractions of the Coadjoint Poincaré algebra

We study a class of extensions of the k-contracted Poincaré algebra under the hipotesis of generalizing the Bargmann algebra and his central charge. As we will see this type of contractions will lead in a natural way to consider the codajoint Poincaré algebra and some of their contractions. Among them there is one such that. considering the quotient of it by a suitable ideal, the (stringy) p-brane Galilei algebra is recovered.

physics.gen-ph↗
arXiv2019

Contractions of the Maxwell algebra

We construct all the possible non-relativistic, non-trivial, Galilei and Carroll k-contractions also known as k-1 p-brane contractions of the Maxwell algebra in $D+1$ space-time dimensions. $k$ has to do with the number of space-time dimensions one is contracting.

hep-th↗
arXiv2018

VSUSY models with Carroll or Galilei invariance

The general method introduced in a previous paperto build up a class of models invariant under generalization of Carroll and Galilei algebra is extended to systems including a set of Grassmann variables describing the spin degree of freedom. The models described here are based on a relativistic supersymmetric algebra with vector and scalar generators (VSUSY) . Therefore, in order to obtain dynamical systems consistent with Carroll or Galilei, we will study the contractions of the anticommuting generators compatible with the Poincaré contractions.

hep-th↗
arXiv2018

Confined dynamical systems with Carroll or Galilei symmetries

We introduce a general method to construct classes of dynamical systems invariant under generalizations of the Carroll and of the Galilei groups. The method consists in starting from a space-time in $D+1$ dimensions and partitioning it in two parts, the first Minkowskian and the second Euclidean. Tha action consist of two terms that are separately invariant the Minkwoskian and Euclidean partitioning. One of those contains a system of lagrangian multiplies that confine the system to a subspace. The other term defines the dynamics of the system. The total lagrangian is invariant under the Carroll or the Galilei groups with zero central charge.

hep-th↗
arXiv2018

The teacher of the gattini (kittens)

The figure of Raoul Gatto, who died in 2017, is remembered here, with an illustration of his career and the main results of his research, along with the personal memories of some of those who worked with him.

physics.hist-ph↗
arXiv2018

Non-relativistic Spinning Particle in a Newton-Cartan Background

We construct the action of a non-relativistic spinning particle moving in a general torsionless Newton-Cartan background. The particle does not follow the geodesic equations, instead the motion is governed by the non-relativistic analog of Papapetrou equation. The spinning particle is described in terms of Grassmann variables. In the flat case the action is invariant under the non-relativistic analog of space-time vector supersymmetry.

hep-th↗
arXiv2014

Conformal symmetry for relativistic point particles: an addendum

We extend the results of our previous work on the conformal invariant description of two relativistic point particles. We consider here the most general lagrangian by using a conformal tensor $h_{μν}$, transforming as a Wilson line, and that allows us to construct invariant expressions for velocities taken at two different space-time points.

hep-th↗