Publications (27)
The Kirillov picture for the Wigner particle
J. M. Gracia-Bondia, F. Lizzi, J. C. Varilly +1
We discuss the Kirillov method for massless Wigner particles, usually (mis)named "continuous spin" or "infinite spin" particles. These appear in Wigner's classification of the unit…
Lattice Gauge Fields and Noncommutative Geometry
A. P. Balachandran, G. Bimonte, G. Landi +2
Conventional approaches to lattice gauge theories do not properly consider the topology of spacetime or of its fields. In this paper, we develop a formulation which tries to remedy…
Fermion Hilbert Space and Fermion Doubling in the Noncommutative Geometry Approach to Gauge Theories
F. Lizzi, G. Mangano, G. Miele +1
In this paper we study the structure of the Hilbert space for the recent noncommutative geometry models of gauge theories. We point out the presence of unphysical degrees of freedo…
Geometry of the Gauge Algebra in Noncommutative Yang-Mills Theory
F. Lizzi, R. J. Szabo, A. Zampini
A detailed description of the infinite-dimensional Lie algebra of star-gauge transformations in noncommutative Yang-Mills theory is presented. Various descriptions of this algebra…
The Zero Tension Limit of The Virasoro Algebra and the Central Extension
F. Lizzi
We argue that the Virasoro algebra for the closed bosonic string can be cast in a form which is suitable for the limit of vanishing string tension. In this form the limit of the Vi…
Mirror Fermions in Noncommutative Geometry
F. Lizzi, G. Mangano, G. Miele +1
In a recent paper we pointed out the presence of extra fermionic degrees of freedom in a chiral gauge theory based on Connes Noncommutative Geometry. Here we propose a mechanism wh…
Noncommutative Lattices and Their Continuum Limits
G. Bimonte, E. Ercolessi, G. Landi +3
We consider finite approximations of a topological space by noncommutative lattices of points. These lattices are structure spaces of noncommutative -algebras which in tur…
From the fuzzy disc to edge currents in Chern-Simons Theory
F. Lizzi, P. Vitale, A. Zampini
We present a brief review of the fuzzy disc, the finite algebra approximating functions on a disc, which we have introduced earlier. We also present a comparison with recent papers…
From Large N Matrices to the Noncommutative Torus
G. Landi, F. Lizzi, R. J. Szabo
We describe how and to what extent the noncommutative two-torus can be approximated by a tower of finite-dimensional matrix geometries. The approximation is carried out for both ir…
String Geometry and the Noncommutative Torus
G. Landi, F. Lizzi, R. J. Szabo
We construct a new gauge theory on a pair of d-dimensional noncommutative tori. The latter comes from an intimate relationship between the noncommutative geometry associated with a…
Entangled Scent of a Charge
M. Asorey, A. P. Balachandran, F. Lizzi +1
We argue that the ground state of a field theory, in the presence of charged particles, becomes an entangled state involving an infinity of soft photons. The quantum field vacuum i…
Distances on a Lattice from Non-commutative Geometry
G. Bimonte, F. Lizzi, G. Sparano
Using the tools of noncommutative geometry we calculate the distances between the points of a lattice on which the usual discretized Dirac operator has been defined. We find that t…
Dynamical Aspects of Lie--Poisson Structures
F. Lizzi, G. Marmo, G. Sparano +1
Quantum Groups can be constructed by applying the quantization by deformation procedure to Lie groups endowed with a suitable Poisson bracket. Here we try to develop an understandi…
Equations of Motion as Constraints: Superselection Rules, Ward Identities
M. Asorey, A. P. Balachandran, F. Lizzi +1
The meaning of local observables is poorly understood in gauge theories, not to speak of quantum gravity. As a step towards a better understanding we study asymptotic (infrared) tr…
Infinitely many star products to play with
J. M. Gracia-Bondia, F. Lizzi, G. Marmo +1
While there has been growing interest for noncommutative spaces in recent times, most examples have been based on the simplest noncommutative algebra: [x_i,x_j]=i theta_{ij}. Here…
Constraints on Unified Gauge Theories from Noncommutative Geometry
F. Lizzi, G. Mangano, G. Miele +1
The Connes and Lott reformulation of the strong and electroweak model represents a promising application of noncommutative geometry. In this scheme the Higgs field naturally appear…
The Fuzzy Disc
F. Lizzi, P. Vitale, A. Zampini
We introduce a finite dimensional matrix model approximation to the algebra of functions on a disc based on noncommutative geometry. The algebra is a subalgebra of the one characte…
Finite Quantum Physics and Noncommutative Geometry
A. P. Balachandran, G. Bimonte, E. Ercolessi +4
Conventional discrete approximations of a manifold do not preserve its nontrivial topological features. In this article we describe an approximation scheme due to Sorkin which repr…
A nonperturbative form of the spectral action principle in noncommutative geometry
H. Figueroa, J. M. Gracia-Bondia, F. Lizzi +1
Using the formalism of superconnections, we show the existence of a bosonic action functional for the standard K-cycle in noncommutative geometry, giving rise, through the spectral…
Universal Landau Pole
A. A. Andrianov, D. Espriu, M. A. Kurkov +1
Our understanding of quantum gravity suggests that at the Planck scale the usual geometry loses its meaning. If so, the quest for grand unification in a large non-abelian group nat…
Quantum Phase Space from String Solitons
F. Lizzi, N. E. Mavromatos
In this paper we view the sigma-model couplings of appropriate vertex operators describing the interaction of string matter with a certain type of string solitons (0-branes) as the…
Lattices and Their Continuum Limits
G. Bimonte, E. Ercolessi, G. Landi +3
We address the problem of the continuum limit for a system of Hausdorff lattices (namely lattices of isolated points) approximating a topological space . The correct framework i…
Inflationary Cosmology from Noncommutative Geometry
F. Lizzi, G. Mangano, G. Miele +1
In the framework of the Connes-Lott model based on noncommutative geometry, the basic features of a gauge theory in the presence of gravity are reviewed, in order to show the possi…
Proceedings to the 'Euroconference on Symmetries Beyond the Standard Model', 12. - 17. July 2003, Portoroz, Slovenia (Part 1 of 2)
P. H. Frampton, A. Melchiorri, L. Bonora +7
Contents of Part 1: 1. Status of the Standard Model(P.H. Frampton), 2. Cosmological Constraints from MBA and Polarization (A. Melchiorri), 3. AdS/CFT Correspondence and Unification…
Matrix Sigma-models for Multi D-brane Dynamics
F. Lizzi, N. E. Mavromatos, R. J. Szabo
We describe a dynamical worldsheet origin for the Lagrangian describing the low-energy dynamics of a system of parallel D-branes. We show how matrix-valued collective coordinate fi…
Noncommutative Lattices as Finite Approximations and Their Noncommutative Geometries
A. P. Balachandran, G. Bimonte, E. Ercolessi +4
Lattice discretizations of continuous manifolds are common tools used in a variety of physical contexts. Conventional discrete approximations, however, cannot capture all aspects o…
Duality Symmetries and Noncommutative Geometry of String Spacetime
F. Lizzi, R. J. Szabo
We examine the structure of spacetime symmetries of toroidally compactified string theory within the framework of noncommutative geometry. Following a proposal of Frohlich and Gawe…