arXiv subjects

F. Lizzi

Publications and source records attributed to F. Lizzi.

At least 19 recordsLinked to original sources

arXiv2018

Entangled Scent of a Charge

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 is altered by the passage of a uniformly moving charge, leaving in its wake a different dressed ground state. In this sense a charged particle leaves its electromagnetic scent even after passing by. Unlike in classical electrodynamics the effect of the charge remains even at infinite time. The calculation is done in detail for the ground state of a spacetime wedge, although the results are more general. This agrees in spirit with recent results over the infrared aspects of field theory, although the technical details are different. These considerations open the possibility that the information carried by quantum fields, being nonlocal, does not disappear beyond the horizon of black holes.

hep-th↗

arXiv2017

The Kirillov picture for the Wigner particle

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 unitary representations of the Poincar\'e group, labelled by elements of the enveloping algebra of the Poincar\'e Lie algebra. Now, the coadjoint orbit procedure introduced by Kirillov is a prelude to quantization. Here we exhibit for those particles the classical Casimir functions on phase space, in parallel to quantum representation theory. A good set of position coordinates are identified on the coadjoint orbits of the Wigner particles; the stabilizer subgroups and the symplectic structures of these orbits are also described.

hep-th↗

arXiv2016

Equations of Motion as Constraints: Superselection Rules, Ward Identities

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) transformation in local quantum physics. Our observables are smeared by test functions, at first vanishing at infinity. In this context we show that the equations of motion can be seen as constraints, which generate a group, the group of space and time dependent gauge transformations.This is one of the main points of the paper. Infrared nontrivial effects are captured allowing test functions which do not vanish at infinity. These extended operators generate a larger group. The quotient of the two groups generate superselection sectors, which differentiate different infrared sectors. The BMS group changes the superselection sector, a result long known for its Lorentz subgroup. It is hence spontaneously broken. Ward identities implied by the gauge invariance of the S-matrix generalize the standard results and lead to charge conservation and low energy theorems. Their validity does not require Lorentz invariance.

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arXiv2013

Universal Landau Pole

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 naturally endowed with the property of asymptotic freedom may also lose its motivation. Instead we propose an unification of all fundamental interactions at the Planck scale in the form of a Universal Landau Pole (ULP), at which all gauge couplings diverge. The Higgs quartic coupling also diverges while the Yukawa couplings vanish. The unification is achieved with the addition of fermions with vector gauge couplings coming in multiplets and with hypercharges identical to those of the the Standard Model. The presence of these particles also prevents the Higgs quartic coupling from becoming negative, thus avoiding the instability (or metastability) of the SM vacuum.

hep-th↗

arXiv2004

Proceedings to the 'Euroconference on Symmetries Beyond the Standard Model', 12. - 17. July 2003, Portoroz, Slovenia (Part 1 of 2)

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 at About 4 TeV (P.H. Frampton), 4. New Solutions in String Field Theory (L. Bonora), 5. The Approach Unifying Spins and Charges (A. Borstnik Bracic and N. Mankoc Borstnik) 6. An Example ... (N. Mankoc Borstnik and H.B. Nielsen) 7. Hierarchy Problem and a New Bound State (C.D. Froggatt and H.B. Nielsen) 8. What Comes Next? (Q. Shafi) 9. Loops Versus Strings (E. Alvarez) 10. Fuzzy Two-dimensional Spaces (F. Lizzi) (Contents of Part 2: 11. Supersymmetric Grandunification and Fermion Masses (B. Bajc) 12. General Principles of Brane Kinematics and Dynamics (M. Pavsic) 13. Cosmological Neutrinos (G. Mangano) 14. The Problem of Mass (C.D. Froggatt) 15. How to Approach Quantum Gravity ... (D. Grumiller and W. Kummer) 16. Hidden Spacetime Symmetries and Generalized Holonomy in M-theory (M.J. Duff and J.T. Liu) 17. On the Resolution of Space-Time Singularities II (M. Maceda and J. Madore) 18. The Multiple Point Principle (D.L. Bennett and H.B. Nielsen) 19. Dynamics of Glue-Balls in N = 1 SYM Theory (L. Bergamin) 20. Quantization of Systems with Continuous Symmetries ... (M.V. Chichikina) 21. Singular Compactifications and Cosmology (L. Jaerv, T. Mohaupt and F. Saueressig) 22. Fundamental Physics and Lorentz Violation (R. Lehnert) 23. Functional Approach to Squeezed States ... (L. Musongela) 24. Constraining the Curvaton Scenario (M. Postma) 25. D-Branes and Unitarity of Noncommutative Field Theories (A. Torrielli) 26. Spinorial Cohomology and Supersymmetry (D. Tsimpis))

hep-ph↗

arXiv2003

From the fuzzy disc to edge currents in Chern-Simons Theory

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 of Balachandran, Gupta and Kürkçüoǧlu, and of Pinzul and Stern, aimed at the discussion of edge states of a Chern-Simons theory.

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arXiv2003

The Fuzzy Disc

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 characterizing the noncommutative plane with a * product and depends on two parameters N and theta. It is composed of functions which decay exponentially outside a disc. In the limit in which the size of the matrices goes to infinity and the noncommutativity parameter goes to zero the disc becomes sharper. We introduce a Laplacian defined on the whole algebra and calculate its eigenvalues. We also calculate the two--points correlation function for a free massless theory (Green's function). In both cases the agreement with the exact result on the disc is very good already for relatively small matrices. This opens up the possibility for the study of field theories on the disc with nonperturbative methods. The model contains edge states, a fact studied in a similar matrix model independently introduced by Balachandran, Gupta and Kurkcuoglu.

hep-th↗

arXiv2001

Infinitely many star products to play with

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 we present new classes of (non-formal) deformed products associated to linear Lie algebras of the kind [x_i,x_j]=ic_{ij}^k x_k. For all possible three-dimensional cases, we define a new star product and discuss its properties. To complete the analysis of these novel noncommutative spaces, we introduce noncompact spectral triples, and the concept of star triple, a specialization of the spectral triple to deformations of the algebra of functions on a noncompact manifold. We examine the generalization to the noncompact case of Connes' conditions for noncommutative spin geometries, and, in the framework of the new star products, we exhibit some candidates for a Dirac operator. On the technical level, properties of the Moyal multiplier algebra M(R_θ^{2n) are elucidated.

hep-th↗

arXiv2001

Geometry of the Gauge Algebra in Noncommutative Yang-Mills Theory

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 are given in terms of inner automorphisms of the underlying deformed algebra of functions on spacetime, of deformed symplectic diffeomorphisms, of the infinite unitary Lie algebra, and of the algebra of compact operators on a quantum mechanical Hilbert space. The spacetime and string interpretations are also elucidated.

hep-th↗

arXiv1999

From Large N Matrices to the Noncommutative Torus

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 irrational and rational deformation parameters by embedding the algebra of the noncommutative torus into an approximately finite algebra. The construction is a rigorous derivation of the recent discretizations of noncommutative gauge theories using finite dimensional matrix models, and it shows precisely how the continuum limits of these models must be taken. We clarify various aspects of Morita equivalence using this formalism and describe some applications to noncommutative Yang-Mills theory.

hep-th↗

arXiv1999

String Geometry and the Noncommutative Torus

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 lattice vertex operator algebra A and the noncommutative torus. We show that the (truncated) tachyon subalgebra of A is naturally isomorphic to a class of twisted modules representing quantum deformations of the algebra of functions on the torus. We construct the corresponding even real spectral triples and determine their Morita equivalence classes using string duality arguments. These constructions yield simple proofs of the O(d,d;Z) Morita equivalences between $d$-dimensional noncommutative tori and give a natural physical interpretation of them in terms of the target space duality group of toroidally compactified string theory. We classify the automorphisms of the twisted modules and construct the most general gauge theory which is invariant under the automorphism group. We compute bosonic and fermionic actions associated with these gauge theories and show that they are explicitly duality-symmetric. The duality-invariant gauge theory is manifestly covariant but contains highly non-local interactions. We show that it also admits a new sort of particle-antiparticle duality which enables the construction of instanton field configurations in any dimension. The duality non-symmetric on-shell projection of the field theory is shown to coincide with the standard non-abelian Yang-Mills gauge theory minimally coupled to massive Dirac fermion fields.

hep-th↗

arXiv1998

Duality Symmetries and Noncommutative Geometry of String Spacetime

We examine the structure of spacetime symmetries of toroidally compactified string theory within the framework of noncommutative geometry. Following a proposal of Frohlich and Gawedzki, we describe the noncommutative string spacetime using a detailed algebraic construction of the vertex operator algebra. We show that the spacetime duality and discrete worldsheet symmetries of the string theory are a consequence of the existence of two independent Dirac operators, arising from the chiral structure of the conformal field theory. We demonstrate that these Dirac operators are also responsible for the emergence of ordinary classical spacetime as a low-energy limit of the string spacetime, and from this we establish a relationship between T-duality and changes of spin structure of the target space manifold. We study the automorphism group of the vertex operator algebra and show that spacetime duality is naturally a gauge symmetry in this formalism. We show that classical general covariance also becomes a gauge symmetry of the string spacetime. We explore some larger symmetries of the algebra in the context of a universal gauge group for string theory, and connect these symmetry groups with some of the algebraic structures which arise in the mathematical theory of vertex operator algebras, such as the Monster group. We also briefly describe how the classical topology of spacetime is modified by the string theory, and calculate the cohomology groups of the noncommutative spacetime. A self-contained, pedagogical introduction to the techniques of noncommmutative geometry is also included.

hep-th↗

arXiv1997

Matrix Sigma-models for Multi D-brane Dynamics

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 fields for the D-branes naturally arise as couplings of a worldsheet sigma-model, and that the quantum dynamics require that these couplings be mutually noncommutative. We show that the low-energy effective action for the sigma-model couplings describes the propagation of an open string in the background of the multiple D-brane configuration, in which all string interactions between the constituent branes are integrated out and the genus expansion is taken into account, with a matrix-valued coupling. The effective field theory is governed by the non-abelian Born-Infeld target space action which leads to the standard one for D-brane field theory.

hep-th↗

arXiv1997

Mirror Fermions in Noncommutative Geometry

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 which provides a high mass to these mirror states, so that they decouple from low energy physics.

hep-th↗

arXiv1997

A nonperturbative form of the spectral action principle in noncommutative geometry

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 action principle, only to the Einstein gravity and Standard Model Yang-Mills-Higgs terms. It provides an effective nonminimal coupling in the bosonic sector of the Lagrangian.

hep-th↗

arXiv1996

Lattice Gauge Fields and Noncommutative Geometry

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 this defect. It starts from a cubical decomposition of the supporting manifold (compactified spacetime or spatial slice) interpreting it as a finite topological approximation in the sense of Sorkin. This finite space is entirely described by the algebra of cochains with the cup product. The methods of Connes and Lott are then used to develop gauge theories on this algebra and to derive Wilson's actions for the gauge and Dirac fields therefrom which can now be given geometrical meaning. We also describe very natural candidates for the QCD theta term and Chern-Simons action suggested by this algebraic formulation. Some of these formulations are simpler than currently available alternatives. The paper treats both the functional integral and Hamiltonian approaches.

hep-lat↗

arXiv1996

Quantum Phase Space from String Solitons

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 quantum phase space of a point particle. The sigma-model is slightly non critical, and therefore one should dress it with a Liouville mode. Quantization is achieved by summing over world-sheet genera (in the pinched approximation). To leading order in the coupling constant expansion, the quantization reproduces the usual quantum mechanical commutator. We attempt to go beyond leading order and we reproduce the generalized string uncertainty principle.

hep-th↗

arXiv1996

Fermion Hilbert Space and Fermion Doubling in the Noncommutative Geometry Approach to Gauge Theories

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 freedom similar to the ones appearing in lattice gauge theories (fermion doubling). We investigate the possibility of projecting out these states at the various levels in the construction, but we find that the results of these attempts are either physically unacceptable or geometrically unappealing.

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