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Proposal for an INFN Research Network (Iniziativa Specifica)
Section I:
Title:
Geometry and Symmetry in Quantum Field Theory
Acronym:
GEOSYM-QFT
National Coordinator (Responsabile Nazionale):
name: Fedele Lizzi
INFN section: Napoli
e-mail: [email protected]
Local Coordinators (Responsabili Locali):
(add as many items as necessary)
! name: Marco Tarlini
INFN section: Firenze
e-mail: [email protected]
! name: Gaetano Fiore
INFN section: Napoli
e-mail: [email protected]
! name: Annalisa Marzuoli
INFN section: Pavia
e-mail: [email protected]
! name: Damiano Anselmi
INFN section: Pisa
e-mail: [email protected]
! name: Massimo Blasone
INFN section: Salerno (Gruppo collegato)
e-mail: [email protected]
Keywords related to the topic of the proposal (up to five):
Geometry, Deformed Symmetries, Noncommutative Geometry, Algebraic and
Topological Quantum Field Theories, Renormalization Techniques in Field Theory
Abstract of the proposal:
The proponents are researchers active in the formal aspects of Quantum Field Theory.
Several of our nodes have a history of joint collaborations in various projects, and
although our main interests as project is in the formal aspects, the competences our
group cover a wide range, from phenomenology to mathematical physics.
The unifying concept behind our project is the use of modern mathematical techniques
to solve various problems in the frontiers of quantum field theory, enabling us to deal
with questions like the quantization of space time, the issue of renormalization,
algebraic and topological quantum field theories.
The main tools are related to symmetries (also deformed) and to the algebraic aspects
of the theory.
The common threads of the collaboration:
Noncommutative geometry and applications to the quantization of spacetime.
Quantum Groups seen as symmetries of quantum spaces.
Quantization Schemes also with tools of statistical mechanics.
Algebraic methods and algebraic geometry, also applied to algebraic and Topological
field theory.
Poisson geometry, Poisson manifolds and in general Poisson structures.
Composition of the participant Research Units:
!
INFN Section Firenze
! Staff members
•
Marco Tarlini
•
Andrea Barducci
•
Francesco Bonechi
•
Riccardo Giachetti
•
Giulio Pettini
! Post-docs, Ph.D. students, Fellows, Senior Researchers
•
Enrico Celegnini
•
Emanuele Sorace
!
INFN Section Napoli
! Staff members
•
Fedele Lizzi
•
Gaetano Fiore
•
Patrizia Vitale
! Post-docs, Ph.D. students, Fellows , Senior Researchers
•
Agostino Devastato
•
Maxim A. Kurkov
•
Antonino Sciarrino
!
INFN Section Pavia
! Staff members
•
Annalisa Marzuoli
•
Mauro Carfora
•
Claudio Dappiaggi
•
Giancarlo Jug
! Post-docs, Ph.D. students, Fellows , Senior Researchers
•
Marco Benini
•
Silvia Bonfanti
•
Dimitri Marinelli
!
INFN Section Pisa
! Staff members
•
Damiano Anselmi
•
Luciano Bracci
•
Paolo Christillin
! Post-docs, Ph.D. students, Fellows, Senior Researchers
•
Ruggero Ferrari
•
Giovanni Morchio
•
Andrea Quadri
•
Franco Strocchi
!
INFN Section Salerno
Staff members
•
Massimo Blasone
•
Federico Corberi
•
Giuseppe Vitiello
! Post-docs, Ph.D. students, Fellows, Senior Researchers
•
Antonio Capolupo
•
Maria Vittoria Gargiulo
•
Gennaro Policastro
!
Section II:
Status of the relevant research field; scientific context, objectives and envisaged
achievements of the proposed network program:
The present context of theoretical physics sees on one side an enormously successful
standard model of particle physics, and on the other a classical theory describing
gravity as the geometry of spacetime. The unification of the two is the present
challenge, and it will probably require a change of paradigm with the introduction of
innovative concepts and tools.
The title of our project: Geometry and Symmetry in Quantum Field Theory, tries to
resume in few words a variety of modern approaches to field theory which
characterizes our project. The role of geometry, algebra and group theory has been
central in the development of quantization of fields, and has provided a guide both form
the conceptual and the phenomenological point of view. Our group covers most of the
current research sectors of Quantum Filed Theory. Although we are mainly active in
the formal aspects, the competences our group cover a wide range of interests from
phenomenology to mathematical physics.
There are common threads that can be seen in our collaboration. The modern study of
symmetries and geometry owes very much to the study of algebraic structures, both
from the point of view of Lie and Hopf algebras, or more generally algebraic geometry.
Algebraic methods are central to the deformation of spaces (noncommutative
geometry) and groups (quantum groups). Several problems in renormalization theory
can be studied using algebraic methods, which also allow us to consider geometric
aspects of non-perturbative Yang-Mills theory. A variety of quantization schemes as
well as tools from statistical field theory applied to spacetime physics are covered.
Our groups have been working at the interaction between topological field theory,
Poisson geometry and noncommutative geometry and more generally on the study of
physical problems taking into account their symmetries and their geometrical
properties.
More in detail we envisage progress along the following lines. These lines are usually
common to more than one section of our collaboration.
The formulation of gravity and field theory is based on a spacetime with continuous and
commuting coordinates, in agreement with intuition. The construction of a quantum
theory of gravity requires a critical reappraisal. Hence the need of a new, more general
kind of geometry, with new, deformed, symmetries. Noncommutative geometry, in its
variants, offers such a tool, and has seen the involvement of more than one node of
our collaboration. A consistent theory of gravity and quantum mechanics is not the only
motivation for NC generalizations of gravity: these can be also useful in addressing
some important issues raised by experimental astrophysical data in the last decade,
and noncommutative geometry has been applied to the standard model of particle
interactions. In this sense the present day high energy physics can be imagined to be
an effective theory of quantum spacetime, where the very geometry is altered.
A key for the lecture of these generalizations of field theory is the spectral properties, at
the basis of noncommutative geometry and its applications to field theory. The metric
information of the theory are in the Dirac operator and its spectrum, from which it is
possible to read the geometrical and physical information, from the metric properties of
the space to the effective action of particles with anomalous magnetic moment to make
but two examples.
The quantization procedure is still an active field of research, especially in its modern
perspectives.
Algebraic and topological field theory, Poisson geometry, noncommutative geometry,
deformation quantization offer different views of the quantization procedure and they
complement each other. They all relate one way or another formal deformation
quantization to operatorial quantization, bridging the differential geometry approach
with the algebraic one. On the other side there are approaches based on Regge
discretization of General Relativity extended to deal with statistical ensembles of Ddimensional triangulated manifolds. More recently similar basic tools have been
employed in quantum information and computing, and in complex network theory, the
slow kinetics of systems with glassy dynamics after the quench to a low temperature
phase.
Gauge invariance has always been a problem in algebraic field theories partly due to
topological effects. Now it is possible to give a fresher look thanks to our better
understanding of functional analytical and geometrical techniques
Symmetries play an important role for renormalization (and renormalizability). Relaxing
Lorentz symmetry has proved to open interesting possibilities for the classification of
power counting renormalizable theories in flat space, but fails for quantum gravity. High
energy processes at LHC have been studied mainly in the Standard Model. It is also
interesting to examine the predictions of nonabelian, nonlinearly realized,
nonrenormalizable gauge models. Another important issue in quantum field theory is
the non-perturbative control of some basic mechanisms of the standard model, such as
gauge and chiral symmetry breaking. We have been studying neutrino mixing and
oscillations in the context of quantum field theory: the main result of our analysis is the
discovery of a condensate structure for the vacuum state associated to the flavor
neutrino fields.
In the last few years there has been a renewed interest in applying field theoretic
methods to condensed matter systems. Topological phases of matter supported by 2
and 3D quantum systems (e.g. graphene and topological insulators) provide
challenging problems for theorists. Another activity is the study of nonequilibrium
statistical mechanics and the slow kinetics of glassy dynamics. In the absence of a
general theory of non-equilibrium the interest is mainly focused on the study of the
dynamical symmetries.
Proposed activities and role of the various Research Units
The methodology of work will be that of a theoretical project. We aim however of not
being a mere sum of individual groups, but to employ our different competences to
enhance our research. Many of us have already a long history of collaborations and
joint participation to conferences and projects. We plan to meet regularly either in an
“ad hoc” conference, or with a space in one of workshop organized by INFN, such as
the Vietri meeting.
FIRENZE
Role of Derived Algebraic Geometry
Derived Algebraic geometry is one the most promising advancements in algebraic
geometry. And in particular investigating the similarities between the generalizations of
stacks (derived algebraic stacks) and moduli spaces. We plan to work out this
dictionary and to exploit this new tool to understand the geometry behind the AKSZ
construction of topological field theories.
Geometric quantization of Poisson structures
We will continue the project of quantization of symplectic groupoids integrating
Poisson-Lie groups and their homogeneous spaces.
Poisson and Courant sigma model
So far the Poisson sigma model in its generality has been studied only on the disk and
with perturbative techniques. We plan to investigate the covariant perturbative
expansion. A very promising approach that we plan to investigate is given by the so
called diagonal brane on the disk, that is equivalent to the model on the sphere.
Dirac operator and spectral properties of fermions.
Within the potential model for mesons already proposed, we will extend our previous
analysis of b\bar{b}) and c\bar{c} to the study of the spectra of B and D mesons and
their hyperfine splittings. (Note the connection with the work in Napoli).
Special functions, Hilbert spaces and Lie algebras
Relations between square integrable functions and Lie groups mediated by special
functions is planned to be extended to other noncompact groups and special functions.
Transport in optical lattices
We want to generalize our studies to bidimensional structures, such as honeycomb
shaped lattices, which are experimentally feasible.
NAPOLI
The Group in Napoli is characterize by the study of noncommutative spaces, deformed
symmetries and field theory. We expect to reach results in the following areas:
- Properties of noncommutative spaces, their symmetries and geometrical, metric and
differential properties. Including also fuzzy spaces.
- Quantum field theories on noncommutative spaces and its twisted symmetries. This
involve also the study of alternative products, beyond the Moyal one.
- Deformed symmetries of gauge theories.
- Applications of noncommutative geometry to the standard model of particle physics,
the spectral action especially in view of the data coming form LHC, as well as its
cosmological consequences. Role of the anomalies for the spectral action.
- Quantization of reducible gauge field theories.
- Study of stability of massless quantum particles, in particular of the graviton.
- Kac-Moody and Borcheds algebras and superalgebras
PAVIA
The Pavia team plans to investigate geometric (Ricci) flows, renormalization group and
QFT landscaping as well as several aspects and applications of Topological Quantum
Field Theory: i) the structure of the moduli space of polyhedral surfaces and its
connection with 2D quantum gravity and matrix models, quantum observables in 3D
TQFT of the BF-type and associated Turaev-Viro SU(2)q state sum models and
(quantum) algorithmic questions related to such items; ii) the physical properties related to the onset of topologically-protected phases and quasi-particles excitations- of
the new forms of condensed matter (graphene mono- and multilayers, graphene cones
and other carbon allotropic curved surfaces).
At the same time, in constructive and algebraic QFT, there is no unanimous
consensus, how topological effects should be included in an axiomatic framework.
Hence an additional goal of our investigation will be to tackle these problems
particularly for gauge theories. Furthermore we shall focus our attention on comparing
our approach to the standard BRST and BV techniques which emphasize the role of
the local algebra of symmetries and their action on the Lagrangian dynamics.
!
PISA!
The group of Pisa is interested in investigating various formal aspects of quantum
mechanics and quantum field theory. Here are our main objectives.!
− Investigate spectra and scattering amplitudes in the lattice theory of massive Yang-Mills
theory, which studies the high energy behavior of nonlinearly realized gauge theories.!
− Study formal properties of the color glass condensate in QCD within the algebraic
approach to the background field method and work out a minimal electroweak
nonlinearly realized theory with scalar resonances.!
− Obtain a non-perturbative control of the infrared structure of the QED S-matrix, and
derive the LSZ reduction formulas.!
− Develop a field-covariant approach to the formulation of perturbative quantum field
theory and study how old and new generating functionals transform under general
perturbative changes of field variables.!
− Study the representations of the Weyl algebra for several configuration spaces.!
− Extend Dollard's procedure to QED, find a LSZ condition for charged asymptotic fields
and explore the possibility of an axiomatic operational formulation of QM.!
− Investigate the interactions of gravitation with matter and question the present
treatment of their detection.!
!
SALERNO
The research activity will continue the activity started in the past years. The research
themes are related among themselves by the common deformed algebraic structure.
Algebraic structures in QFT
Especially in connection with flavor mixing and the contribution to dark energy and dark
matter coming from neutrino mixing as well as Lorentz invariance violation. We will
further study the entanglement associated to neutrino mixing and quantum information.
Results on the deformed Hopf algebra and the doubling of the degrees of freedom,
obtained in past research projects, will be applied to the analysis of Connes’
noncommutative spectral geometry, also in collaboration with the Napoli node.
Nonlinear dynamics, phase transitions and interdisciplinary applications
We will continue the study of the kinetics of disordered magnets. In a recent series of
papers we have used renormalization group and scaling ideas to describe the
dynamics. We found: i) the absence of the superuniversality property and ii) an
interplay between an evolution with a logarithmically slow behavior and another
described by power laws. This has been identified in special topological properties of
the fractal substrate. We will keep consider other systems and continue to study the
problem of the kinetics on generic graphs in order to uncover the role of the substrate
topology and the kinetics of models of glassy systems, such as spin glasses and
kinetically constrained models.
Section III:
List of the most significant publications of the last five years of each Research
Unit related to the proposal (10 publications for each Unit, inverse chronological
order):
!
INFN Section Firenze
1) E. Celeghini, Ş. Kuru, J. Negro, M.A. del Olmo
"A unified approach to quantum and classical TTW systems based on
factorizations"
ANNALS OF PHYSICS Volume: 332 Pages: 27-37
DOI: 10.1016/j.aop.2013.01.008 Publisced: MAY 2013
2) Barducci A., Giachetti R.
"Effective action for fermions with anomalous magnetic moment from FoldyWouthuysen transformation"
MODERN PHYSICS LETTERS A Volume: 28 Issue: 9 Article Number:
1350029
DOI: 10.1142/S0217732313500296 Published: MAR 21 2013
3) Giachetti R., Sorace E.
"Unified covariant treatment of hyperfine splitting for heavy and light mesons"
PHYSICAL REVIEW D Volume: 87 Issue: 3 Article Number: 034021
DOI: 10.1103/PhysRevD.87.034021 Published: FEB 13 2013
4) Julen Ibanez-Azpiroz, Asier Eiguren, Aitor Bergara, Giulio Pettini, Michele
Modugno
"Tight binding models for ultracold atoms in honeycomb optical lattices"
PHYSICAL REVIEW A Volume: 87 Issue: 1 Article Number: 011602
DOI: 10.1103/PhysRevA.87.011602 Published: JAN 9 2013
5) Bonechi F., Ciccoli N., Staffolani N., Tarlini M.
"The quantization of the symplectic groupoid of the standard Podles sphere"
JOURNAL OF GEOMETRY AND PHYSICS Volume: 62 Issue: 8 Pages:
1851-1865
DOI: 10.1016/j.geomphys.2012.04.001 Published: AUG 2012
6) Giachetti R., Grecchi V.
"PT-symmetric operators and metastable states of the 1D relativistic
oscillators"
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL Volume:
44 Issue: 9 Article Number: 095308
DOI: 10.1088/1751-8113/44/9/095308 Published: MAR 4 2012
7) Bonechi F., Cattaneo A. S., Mnev P.
"The Poisson sigma model on closed surfaces"
JOURNAL OF HIGH ENERGY PHYSICS Issue: 1 Article Number: 099
DOI: 10.1007/JHEP01(2012)099 Published: JAN 2012
8) Bonechi F., Mnev P., Zabzine M.
"Finite-Dimensional AKSZ-BV Theories"
LETTERS IN MATHEMATICAL PHYSICS Volume: 94 Issue: 2 Pages:
197-228
DOI: 10.1007/s11005-010-0423-3 Published: NOV 2010
9) Bonechi F., Zabzine M.
"Poisson Sigma Model on the Sphere"
COMMUNICATIONS IN MATHEMATICAL PHYSICS Volume: 285 Issue: 3
Pages: 1033-1063
DOI: 10.1007/s00220-008-0615-1 Published: FEB 2009
10) Bonechi F., Ciccoli N., Staffolani N., Tarlini M.
"On the integration of Poisson homogeneous spaces"
JOURNAL OF GEOMETRY AND PHYSICS Volume: 58 Issue: 11 Pages:
1519-1529
DOI: 10.1016/j.geomphys.2008.07.001 Published: NOV 2008
!
INFN Section Napoli
1) On quantum mechanics with a magnetic field on R**n and on a torus T**n,
and their relation
Gaetano Fiore. 2013. 20 pp.
Published in Int.J.Theor.Phys. 52 (2013) 877-896
2) Spectral action, Weyl anomaly and the Higgs-Dilaton potential
A.A. Andrianov (St. Petersburg State U. & Barcelona U., ECM & ICC, Barcelona
U.), M.A. Kurkov (Naples U. & INFN, Naples), Fedele Lizzi (Barcelona U., ECM
& ICC, Barcelona U. & Naples U. & INFN, Naples). Jun 2011. 24 pp.
Published in JHEP 1110 (2011) 001
3) Quantum Corrections in the Group Field Theory Formulation of the EPRL/FK
Models
Thomas Krajewski (Orsay, LPT & Marseille, CPT), Jacques Magnen (Ecole
Polytechnique, CPHT & Orsay, LPT), Vincent Rivasseau (Orsay, LPT), Adrian
Tanasa (Ecole Polytechnique, CPHT & Bucharest, IFIN-HH), Patrizia Vitale
(Orsay, LPT & Naples U. & INFN, Naples). Jul 2010. 34 pp.
Published in Phys.Rev. D82 (2010) 124069
4) Noncommutative gauge theory and symmetry breaking in matrix models
Harald Grosse (Vienna U.), Fedele Lizzi (Naples U. & INFN, Naples & ICC,
Barcelona U.), Harold Steinacker (Vienna U.). Jan 2010. 29 pp.
Published in Phys.Rev. D81 (2010) 085034
5) On second quantization on noncommutative spaces with twisted symmetries
Gaetano Fiore (IAM, Naples & INFN, Naples). 38 pp.
Published in J.Phys. A43 (2010) 155401
6) Noncommutative spacetimes: symmetries in noncommutative geometry and
field theory
P Aschieri, M Dimitrijević, P Kulish, F Lizzi, J Wess
Springer Lecture Notes in Physics 774 (2009)
7) Translation Invariance, Commutation Relations and Ultraviolet/Infrared
Mixing
Salvatore Galluccio (Naples U. & INFN, Naples), Fedele Lizzi (Naples U. &
INFN, Naples & ICC, Barcelona U.), Patrizia Vitale (Naples U. & INFN, Naples).
Jul 2009. 24 pp.
Published in JHEP 0909 (2009) 054
8) Twisting all the way: From Classical Mechanics to Quantum Fields
Paolo Aschieri (Enrico Fermi Ctr., Rome & Piemonte Orientale U., Alessandria
& INFN, Turin), Fedele Lizzi, Patrizia Vitale (Naples U. & INFN, Naples). Aug
2007. 32 pp.
Published in Phys.Rev. D77 (2008) 025037
9) Twisted Noncommutative Field Theory with the Wick-Voros and Moyal
Products
Salvatore Galluccio, Fedele Lizzi, Patrizia Vitale (Naples U. & INFN, Naples).
Sep 2008. 34 pp.
Published in Phys.Rev. D78 (2008) 085007
10) On full twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
Gaetano Fiore (IAM, Naples & INFN, Naples & Munich U.), Julius Wess
(Munich U. & Munich, Max Planck Inst. & Hamburg U., Inst. Theor. Phys. II &
DESY). Jan 2007. 21 pp.
Published in Phys.Rev. D75 (2007) 105022
!
INFN Section Pavia
1) M Benini, C Dappiaggi, A Schenkel Quantized Abelian principal connections
on Lorentian manifolds, arXiv:1303.2515 [math-ph]
2) G Jug, M Paliienko, Multilevel tunneling sytems and fractal clustering in the
low-temperature mixed Alkali-Silicate glasses, arXiv: 1301.7233 [cond-mat.disnn], The Scient. World Jour. (to appear)
3) M Carfora, A Marzuoli Quantum Triangulations: Moduli spaces, Strings, and
Quantum Computing, Lecture Notes in Physics 845 (295 pp.) Springer-Verlag,
Berlin-Heidelberg (2012)
4) A Marzuoli, G Palumbo, BF-Theory in graphene: a route toward topological
quantum computing?, Europhys. Lett. 99 (2012) 10002, arXiv: 1111.1593v2
[quant-ph]
5) C Dappiaggi, G Lechner, E Morfa-Morales, Deformation of quantum field
theories on spacetimes with Killing vector fields, Commun. Math. Phys. 305
(2011) 99-130, arXiv:1006.3548 [math-ph]
6) M Carfora, Ricci flow conjugate initial data sets for Einstein equations, Adv.
Theor. Math. Phys. 15 (2011) 1411-1484,arXiv:1006.1500 [gr-qc]
7) C Dappiaggi, N Pinamonti, M Porrmann, Local causal structures, Hadamard
states and the principle of local covariance in quantum field theory, Commun.
Math. Phys. 304 (2011) 459-498, arXiv:1001.0858 [math-ph]
8) M Carfora, A Marzuoli, M Rasetti, Quantum tetrahedra, J. Phys. Chem. A 113
(2009) 15376-15383, arXiv : 1001.4402 [math-ph]
9) E Granato, G Jug, Spin-size disordered models for granular superconductors
with charging effects, Physica B 404 (2009) 2916, arXiv: 0907.3120 [condmat.supr-con]
10) M Carfora, T Buchert, On the curvature of the present day universe, Class.
Quant. Grav. 25 (2008) 195001, arXiv:0803.1401 [gr-qc]
INFN Section Pisa
1. D. Anselmi, Properties of the classical action of quantum gravity, JHEP 1305 (2013)
028, Doi 10.1007/JHEP05(2013)028, arXiv:1302.7100 [gr-qc]!
!
2. L. Barattini, P. Christillin, The Machian origin of the centrifugal force , Journal of
Modern Physics (2012) 3, 1298!
!
3. D. Binosi, A. Quadri, The Background Field Method as a Canonical Transformation,
Published in Phys.Rev. D85 (2012) 121702, DOI: 10.1103/PhysRevD.85.121702,
arXiv:1203.6637 [hep-th]!
!
4. L. Bracci and L. E. Picasso, On the Weyl algebra for a particle on a sphere, Eur.
Phys. J. Plus 126: 4 (2011)!
!
5. P. Christillin, Speakable and unspeakable in cosmology: Dark matter vs. gravitational
self-energies. Hubble’s constant, the cosmological term and all that, Eur. Phys. J. Plus
(2011) 126: 88, DOI: 10.1140/epjp/i2011-11088-6!
!
6. L. Bracci and L. E. Picasso, On the identity of some von Neumann algebras and
some consequences, Lett. Math. Phys. 93:267-277 (2010)!
!
7. D. Anselmi , Standard Model without elementary scalars and high energy Lorentz
violation, Eur.Phys.J. C65 (2010) 523-536 and arXiv:0904.1849 [hep-ph]!
!
8. D. Bettinelli, R. Ferrari, A. Quadri, A Massive Yang-Mills Theory based on the
Nonlinearly Realized Gauge Group, Phys.Rev. D77 (2008) 045021, DOI:
10.1103/PhysRevD.77.045021, arXiv:0705.2339 [hep-th]!
!
9. G. Morchio, F.Strocchi, Classical and Quantum Mechanics from the Universal
Poisson-Rinehart algebra of a manifold, Reports on Math. Phys. 64, 33 (2009)!
!
10. G. Morchio e F. Strocchi, Chiral symmetry breaking and theta vacuum structure in
QCD, Ann. Phys. 324, (2009) 2236-2254!
!
!
INFN Section Salerno
1) M. V. Gargiulo, M. Sakellariadou, G. Vitiello, Doubling of the Algebra and Neutrino
Mixing within Noncommutative Spectral Geometry, arXiv:1305.0659 [hep-th]
!
2) A.Capolupo, W. J. Freeman and G. Vitiello, Dissipation of 'dark energy' by cortex in
knowledge retrieval, Phys. of Life Reviews 10, 85 (2013)
3) F. Corberi, G. Gonnella, A. Piscitelli, and M. Zannetti “Heat exchanges in a
quenched ferromagnet”, J. Phys. A: Math. Theor. 46, 042001 (2013).
4) R. Burioni, F. Corberi, and A. Vezzani, “Topological regulation of activation barriers
on fractal substrates”, Phys. Rev. E 87, 032160 (2013).
5) F. Corberi, E. Lippiello, A. Mukherjee, S. Puri, M. Zannetti, Crossover in Growth Law
and Violation of Superuniversality in the Random Field Ising Model, Phys. Rev. E 85,
021141 (2012)
6) S. Ahmad, F. Corberi, S.K. Das, E. Lippiello, S. Puri, and M. Zannetti “Aging and
crossovers in phase-separating fluid mixtures”, Phys. Rev. E 86, 061129 (2012).
7) M. Blasone and P. Jizba, Nambu-Goldstone dynamics and generalized coherentstate functional integrals, J.Phys. A45 (2012) 244009
8) M. Sakellariadou, A. Stabile, G. Vitiello, Noncommutative spectral geometry,
algebra doubling and the seeds of quantization, Phys. Rev. D84 (2011) 045026
9) M. Blasone, M. Di Mauro and G. Vitiello, Non-abelian gauge structure in neutrino
mixing, Physics Letters B 697 (2011) 238
10) M. Blasone, A. Capolupo, C.-R. Ji and G. Vitiello, On flavor conservation in weak
interaction decays involving mixed neutrinos, Int. J. of Modern Physics A 25 (2010)
4179
List of the main international collaborations related to the proposal:
Firenze:
Maxim Zabzine
Dep. of Theo. Phys. Uppsala, Sweden
Alberto Cattaneo
Inst. fur Mathematik Univ. Zurich, Switzerland
Alejandro Cabrera
Dep. de Matematica Aplicada, Inst. de Matematica, Univ. Federal do Rio de Janeiro,
Brasil
Mariano Del Olmo
Dep. de Fisica Teorica, Univ. di Valladolid, Spain
Michele Modugno
Univ Basque Country UPV EHU, Dept Theoret Phys & Hist Sci, Bilbao, Spain
Napoli
A. Andrianov
University of Sankt Petersburgh, Russia
D. Espriu
Universitat de Barcelona, Spain
Jacques Magnen
Ecole Polytechnique, CPHT & Orsay, LPT
Thomas Krajewski
Orsay, LPT & Marseille, CPT, France
V. Rivasseau
LPTH Orsay, France
Adrian Tanasa
Ecole Polytechnique, CPHT France & Bucharest, IFIN-HH Romania
J.C. Wallet
CNRS Orsay, France
Pavia
K Fredenhagen
DESY
J Yngvason
Schrodinger Institute Vienna
A. Iorio
Charles University (Prague)
T. Buchert
Université de Lyon
J. Pachos, G. Palumbo
Leeds University
Ko Sanders
E. Fermi Institute
G. Lechner
Leipzig
A. Schenkel, H Gottschalk
Wuppertal
R Littlejohn, R van der Veen
UC Berkeley
PISA
Daniele Binosi e Dionysis Triantafyllopoulos,
ECT, Trento
Detlev Buchholz,
Università di Goettingen, Germany
Costantino Budroni,
Università di Siegen, Germany
Giuseppe De Nittis,
Friedrich-Alexander-Uni Erlangen, Germany
Stefan Dittmaier,
Physikalisches Institut, Albert-Ludwigs Universitaet Freiburg, Germany
Edmond Iancu,
Institut de Physique Theorique, CEA-Saclay, France
Andrei Slavnov,
Steklov Mathematical Institute, Moscow, Russia
SALERNO
Mairi Sakellariadou
King's College, London, UK.
Petr Jizba
Prague Technical University, Czech Republic.
A.Beige
Leeds University, UK.
L.F. Cugliandolo
Paris VI, France.
S. Puri,
Dehli, India.
S. Das
Bangalore, India.
W. J. Freeman
Berkeley, USA.
L. Montagnier
UNESCO, Paris, France