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Roberto Casalbuoni

Publications and source records attributed to Roberto Casalbuoni.

At least 37 records · Page 2Linked to original sources
arXiv2014

Conformal symmetry for relativistic point particles

In this paper we consider the conformal dynamics for a system of $N$ interacting relativistic massless particles. A detailed study is done for the case of two-particles, with a particular attention to the symmetries of the problem. In fact, we show that this analysis could be extended to the case of higher spin symmetries. Always in the two particle case a formulation in terms of bilocal fields is proposed. For a system of $N$ particles we consider two possible scenarios: i) action invariant under any permutation of the $N$ particles. This case corresponds to completely democratic interactions with each particle interacting with all the others. The action depends on $N-1$ dimensionless coupling constants. ii) By putting the particles along a one-dimensional lattice (open or closed) with nearest neighbor interactions, one obtains a model with only two-body interactions depending on a single dimensionless coupling. This model can be easily extended to the continuum case, obtaining a conformal string-like (closed or open) system.

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arXiv2014

Crystalline color superconductors

Inhomogeneous superconductors and inhomogeneous superfluids appear in a variety of contexts including quark matter at extreme densities, fermionic systems of cold atoms, type-II cuprates, and organic superconductors. In the present review the focus is on properties of quark matter at high baryonic density, which may exist in the interior of compact stars. The conditions realized in these stellar objects tend to disfavor standard symmetric BCS pairing and may favor an inhomogeneous color superconducting phase. The properties of inhomogeneous color superconductors are discussed in detail and in particular of crystalline color superconductors. The possible astrophysical signatures associated with the presence of crystalline color superconducting phases within the core of compact stars are also reviewed.

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arXiv2011

Space-time transformations of the Born-Infeld gauge field of a D-brane

Recently Gliozzi has shown that, under certain conditions, it is possible to derive the Dirac-Born-Infeld action for an abelian gauge field of a D-brane. Also, the action turns out to be invariant with respect to a non-linear realization of the full Poincaré group. A crucial role is played by the transformation properties of the gauge field under the non-linear realization. The aim of this note is to point out that these transformation properties are derived directly from the gauge fixing of the diffeomorphisms of the brane and the necessary compensating reparametrization when one performs a Lorentz transformation.

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arXiv2010

SuperParticle realization of twisted N=2 SUSY algebra

We construct a pseudoclassical particle model associated to the twisted N=2 SUSY algebra in four dimensions. The particle model has four kappa symmetries. Three of them can be used to reduce the model to the vector supersymmetry particle case. The quantization of the model gives rise to two copies of the 4d Dirac equation. The kappa symmetries result to be associated to 4 TSUSY invariant bilinear odd operators who are null operators when a particular condition is satisfied. These operators are in correspondence one to one with analogous operators existing in the case of the N=2 SUSY algebra, making both cases 1/2 BPS.

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arXiv2010

On aspects of self-consistency in the Dyson-Schwinger approach to QED and λ(ϕ^\star ϕ)^2 theories

We investigate some aspects of the self-consistency in the Dyson-Schwinger approach to both the QED and the self-interacting scalar field theories. We prove that the set of the Dyson-Schwinger equations, together with the Green-Ward-Takahashi identity, is equivalent to the analogous set of integral equations studied in condensed matter, namely many-body perturbation theory, where it is solved self-consistently and iteratively. In this framework, we compute the non-perturbative solution of the gap equation for the self-interacting scalar field theory.

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arXiv2010

Field Representations of Vector Supersymmetry

We study some field representations of vector supersymmetry with superspin Y=0 and Y=1/2 and nonvanishing central charges. For Y=0, we present two multiplets composed of four spinor fields, two even and two odd, and we provide a free action for them. The main differences between these two multiplets are the way the central charge operators act and the compatibility with the Majorana reality condition on the spinors. One of the two is related to a previously studied spinning particle model. For Y=1/2, we present a multiplet composed of one even scalar, one odd vector and one even selfdual two-form, which is a truncation of a known representation of the tensor supersymmetry algebra in Euclidean spacetime. We discuss its rotation to Minkowski spacetime and provide a set of dynamical equations for it, which are however not derived from a Lagrangian. We develop a superspace formalism for vector supersymmetry with central charges and we derive our multiplets by superspace techniques. Finally, we discuss some representations with vanishing central charges.

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arXiv2009

Vector Supersymmetry from OSp(3,2|2): Casimir Operators

In this paper we briefly review the main results obtained in arXiv:0812.1982, where some algebraic properties of the 'vector supersymmetry' (VSUSY) algebra have been studied. VSUSY is a graded extension of the Poincare' algebra in 4 dimensions with two central charges. We derive all independent Casimir operators of VSUSY and we find two distinct spin-related operators in the case of nonvanishing central charges. One is the analogue of superspin for VSUSY and the other is a new spin, called C-spin, whose value is fixed to 1/2. We also show that the VSUSY algebra and its Casimir operators can be derived by an Inonu-Wigner contraction from OSp(3,2|2). This paper is based on the talk given in Varna, Bulgaria, during the 4-th EU RTN Workshop 2008.

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arXiv2008

Vector Supersymmetry: Casimir operators and contraction from OSp(3,2|2)

We study some algebraic properties of the 'vector supersymmetry' (VSUSY) algebra, a graded extension of the four-dimensional Poincare' algebra with two odd generators, a vector and a scalar, and two central charges. The anticommutator between the two odd generators gives the four-momentum operator, from which the name vector supersymmetry. We construct the Casimir operators for this algebra and we show how both algebra and Casimirs can be derived by contraction from the simple orthosymplectic algebra OSp(3,2|2). In particular, we construct the analogue of superspin for vector supersymmetry and we show that, due to the algebraic structure of the Casimirs, the multiplets are either doublets of spin (s,s+1) or two spin 1/2 states. Finally, we identify an odd operator, which is an invariant in a subclass of representations where a BPS-like algebraic relation between the mass and the values of the central charges is satisfied.

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arXiv2008

Space-time Vector Supersymmetry and Massive Spinning Particle

We construct the action of a relativistic spinning particle from a non-linear realization of a space-time odd vector extension of the Poincaré group. For particular values of the parameters appearing in the lagrangian the model has a gauge world-line supersymmetry.{As a consequence of this local symmetry there are BPS solutions in the model preserving 1/5 of the supersymmetries.} A supersymmetric invariant quantization produces two decoupled 4d Dirac equations.

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arXiv2007

Exotic Non-relativistic String

We construct a classical non-relativistic string model in 3+1 dimensions. The model contains a spurion tensor field that is responsible for the non-commutative structure of the model. Under double dimensional reduction the model reduces to the exotic non-relativistic particle in 2+1 dimensions.

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arXiv2006

Majorana and the Infinite Component Wave Equations

I review the paper of Majorana about relativistic particles with arbitrary spin written in 1932. The main motivation for this papers was the dissatisfaction about the negative energy solutions of the Dirac equation. As such, the paper became immediately obsolete due to the almost contemporaneous discovery of the positron. However, for the first time, the unitary representations of the Lorentz group were introduced. Majorana considered two particular representations (named, after him, Majorana representations) which enjoy many interesting properties. A discussion about the reasons for its revival in the 60's is presented.

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arXiv2006

QCD critical point: a historical perspective

We review the history of the critical point in the QCD phase diagram, baryon density vs. temperature. In particular we discuss the different theoretical approaches to this problem.

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arXiv2006

Color Superconductivity in High Density QCD

We describe the effects of the strange quark mass and of color and electric neutrality on the superconducing phases of QCD. We discuss various phases pointing out the corresponding problems, typically arising from a chromomagnetic instability. We show that, at least for particular configurations, the LOFF phase dominates over the gCFL phase, when close to the transition from gCFL to the normal phase.

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arXiv2004

Little Higgs Models and Precision Electroweak Data

We study the low energy limit of Little Higgs models. The method consists in eliminating the heavy fields using their classical equations of motion in the infinite mass limit. After the elimination of the heavy degrees of freedom we can directly read off deviations from the precision electroweak data. We also examine the effects on the low energy precision experiments.

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arXiv2003

Inhomogeneous Superconductivity in Condensed Matter and QCD

Inhomogeneous superconductivity arises when the species participating in the pairing phenomenon have different Fermi surfaces with a large enough separation. In these conditions it could be more favorable for each of the pairing fermions to stay close to its Fermi surface and, differently from the usual BCS state, for the Cooper pair to have a non zero total momentum. For this reason in this state the gap varies in space, the ground state is inhomogeneous and a crystalline structure might be formed. This situation was considered for the first time by Fulde, Ferrell, Larkin and Ovchinnikov, and the corresponding state is called LOFF. The spontaneous breaking of the space symmetries in the vacuum state is a characteristic feature of this phase and is associated to the presence of long wave-length excitations of zero mass. The situation described here is of interest both in solid state and in elementary particle physics, in particular in Quantum Chromo-Dynamics at high density and small temperature. In this review we present the theoretical approach to the LOFF state and its phenomenological applications using the language of the effective field theories.

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arXiv2003

Anisotropic Color Superconductivity

We discuss the possibility that in finite density QCD an anisotropic phase is realized. This case might arise for quarks with different chemical potential and/or different masses. In this phase crystalline structures may be formed. We consider this possibility and we describe, in the context of an effective lagrangian, the corresponding phonons as the Nambu-Goldstone bosons associated to the breaking of the space symmetries.

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arXiv2001

A theory of algebraic integration

In this paper we extend the idea of integration to generic algebras. In particular we concentrate over a class of algebras, that we will call self-conjugated, having the property of possessing equivalent right and left multiplication algebras. In this case it is always possible to define an integral sharing many of the properties of the usual integral. For instance, if the algebra has a continuous group of automorphisms, the corresponding derivations are such that the usual formula of integration by parts holds. We discuss also how to integrate over subalgebras. Many examples are discussed, starting with Grassmann algebras, where we recover the usual Berezin's rule. The paraGrassmann algebras are also considered, as well as the algebra of matrices. Since Grassmann and paraGrassmann algebras can be represented by matrices we show also that their integrals can be seen in terms of traces over the corresponding matrices. An interesting application is to the case of group algebras where we show that our definition of integral is equivalent to a sum over the unitary irreducuble representations of the group. We show also some example of integration over non self-conjugated algebras (the bosonic and the $q$-bosonic oscillators), and over non-associative algebras (the octonions).

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