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Contributions
Links to the contributions are provided after each abstract. All presentations are less than 1Mb in size, with the exceptions
of Prof. Lukierski (30Mb), Prof. Madore (5.6Mb), Prof. Reuter (14Mb) and Prof. Woronowicz (17Mb), where zip archives of pictures of the
slides are provided. Pictures of speakers are links to larger pictures.
You may download single zipfile (76Mb) containing all the contributions.
Falsifiable noncommutative field theories of not everything (Giovanni Amelino Camelia)
 | This appears to be a time of transition for theory research
in fundamental physics. The weaknesses of the myth of a theory
of everything, to be adopted exclusively on the basis of its
conceptual compellingness, finally start to be widely acknowledged.
I shall discuss some possible formulations of field theory in
noncommutative spacetime as examples of application of
a completely alternative strategy for research on the Planck-scale
realm, in which one attempts to only address some aspects
of the quantum-gravity problem but requiring that the framework
be readily subject to experimental tests.
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[link as http://www.mat.uniroma2.it/08QSTNG/Amelino-Camelia]
Symmetries and dynamics of noncommutative spaces (Paolo Aschieri)
 | We study a wide class of noncommutative manifolds and their quantum Lie algebra of infinitesimal diffeomeorphisms. In this way, symmetries principles can be implemented. We consider the example of general covariance in noncommutative spacetime that leads to a noncommutative gravity theory. The issue of Noether theorem for noncommutative field theories is addressed and answered by introducing a dynamical star-product.
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[link as http://www.mat.uniroma2.it/08QSTNG/Aschieri]
On the inequivalence of Euclidean and Minkowskian methods on Moyalspace (Dorothea Bahns)
 | A comparison of certain graphs of noncommutative bosonic field theory shows that the perturbative calculations performed in the popular framework of Euclidean field theory on Moyal space (with nondegenerate noncommutativity matrix) tell us very little about the renormalization of theories with a Lorentzian signature. I will show that the Euclidean method employed is in fact unrelated to the known Lorentzian frameworks (on Moyal space with nondegenerate noncommutativity matrix).
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[link as http://www.mat.uniroma2.it/08QSTNG/Bahns]
Causality on the Moyal Plane (Aiyalam Balachandran)
 | Quantum field theories can be formulated on the Moyal plane with the Poincare\' group acting with a twisted coproduct.Such theories are nonlocal and violate causality.Such violation has consequences for Lorentz invariance of the S-matrix,CPT theorem, correlations of observables at space-like distances ,the fluctuation-dissipation theorem and CMB spectrum. The talk reviews some aspects of these consequences of non-causality.
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[link as http://www.mat.uniroma2.it/08QSTNG/Balachandran]
Warped Convolutions: A novel tool in the construction of QFTs (Detlev Buchholz)
 | Recently, Grosse and Lechner introduced a novel deformation procedure for non-interacting quantum field theories, giving rise to interesting examples of wedge-localized quantum fields with a non-trivial scattering matrix. In this talk we outline an extension of this procedure to the general framework of quantum field theory by introducing the concept of warped convolutions: given a theory, this construction provides wedge-localized operators which commute at spacelike distances, transform covariantly under the underlying representation of the Poincare group and admit a scattering theory. The corresponding scattering matrix is nontrivial but breaks the Lorentz symmetry, in spite of the covariance and wedge-locality properties of the deformed operators.
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[link as http://www.mat.uniroma2.it/08QSTNG/Buchholz]
The reconstruction theorem in noncommutative geometry (Alain Connes)
 | We show that the first five of the axioms we had formulated
on spectral triples suffice (in a slightly stronger form) to
characterize the
spectral triples associated to smooth compact manifolds. The algebra,
which is
assumed to be commutative, is shown to be isomorphic to the algebra of all
smooth functions on a unique smooth oriented compact manifold, while the
operator is shown to be of Dirac type and the metric to be Riemannian.
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[link as http://www.mat.uniroma2.it/08QSTNG/Connes]
The C*-algebra ssociated with an integral domain (Joachim Cuntz)
 | Let R be an integral domain (i.e. a commutative ring without zero-divisors). Using the addition and multiplication in R in a natural way, associate with R a C*-algebra A[R]. This algebra is simple purely infinite and is closely related to the structure of the prime ideals in R.
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[link as http://www.mat.uniroma2.it/08QSTNG/Cuntz]
Quantum projective plane: holomorphic calculus and spectral geometry (Ludwik Dabrowski)
 | The algebra of antiholomorhic forms on the quantum projective plane CPq(2) is constructed.
The associated Dolbeault-Dirac operator defines
a 0-dimensional Uq(su(3))-equivariant even spectral triple.
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[link as http://www.mat.uniroma2.it/08QSTNG/Dabrowski]
Kinematical Uniqueness of Loop Quantum Gravity (Christian Fleischhack)
 | We review uniqueness results for the kinematical part of loop quantum gravity. After sketching the general loop formalism, the holonomy-flux and the Weyl algebras are introduced. In both cases, then, diffeomorphism invariant representations are described. Finally, the basic ideas for the proof of their uniqueness are given.
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[link as http://www.mat.uniroma2.it/08QSTNG/Fleischhack]
Quantum coordinates of an event (Klaus Fredenhagen)
 | The strongest argument for a noncommutative structure of spacetime arises from the noncommutative structure of observables in quantum physics. We determine the corresponding structure within conventional quantum field theory and within quantum field theory on quantum spacetime.
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[link as http://www.mat.uniroma2.it/08QSTNG/Fredenhagen]
Attempts towards standard model in Moyal spacetimes. (T. R. Govindarajan)
 | We will describe attempts to construct gauge theories in Moyal spacetimes preserving twisted Poincare symmetry. Specifically we will consider spontaneous symmetry breakdown and gauge boson mass generation. We will indicate our attempts to construct standard model
in such a spacetime.
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[link as http://www.mat.uniroma2.it/08QSTNG/Govindarajan]
On Spectral Triples of Holonomy Loops (Jesper Grimstrup)
 | In my talk I will show how a semifinite spectral triple is obtained from a rearrangement of central elements of Loop Quantum Gravity. The triple is based on a countable set of graphs and the algebra consists of holonomy loops in this set. The Dirac type operator resembles a global functional derivation operator. The interaction between the algebra of holonomy loops and the Dirac type operator reproduces the structure of the Poisson bracket of General Relativity. In the talk I will argue how one might obtain a Hamilton constraint from the spectral triple construction.
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[link as http://www.mat.uniroma2.it/08QSTNG/Grimstrup]
 | NCQFT suffers from the infrared ultraviolet mixing. We found two ways to cure the disease. The first way, with Raimar Wulkenhaar, consists in adding a local term violating translation invariance. The RG flow becomes bounded and the Landau ghost problem is cured.
The second way, with Fabien Vignes-Tourneret,
consists in adding a nonlocal term respecting tranlation symmetry.
We formluate nc fermions and nc gauge models.
We comment on a modification of the properties of the QFT in the nc setting and observe, with Gandalf Lechner, that certain fields obey a wedge locality.
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[link as http://www.mat.uniroma2.it/08QSTNG/Grosse]
Monopoles and instantons on quantum projective spaces (Giovanni Landi)
 | Aiming at the construction of physical models, we describe all self-dual monopole connections and some self-dual instanton connections on the quantum projective plane.
We also describe monopoles on the quantum projective lines and associated gauged Laplacian operators.
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[link as http://www.mat.uniroma2.it/08QSTNG/Landi]
NC Field Theory with the Moyal and Wick-Voros products: Twist and S-matrix (Fedele Lizzi)
 | In this work in collaboration with Vitale and Galluccio I will construct a quartic field theory based with the Wick (or Voros or normal ordered) product and compare it with the known theory based with the Moyal product. The two theories appear to be different at the level of their Green\'s function. When the analysis is carried over at the level of the physically relevant S-matrix, in the twist deformed context, we show that the amplitudes are the same.
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[link as http://www.mat.uniroma2.it/08QSTNG/Lizzi]
K-deformations of oscillators, k-deformed quantum fields and k-deformed Fock sp. (Jerzy Lukierski)
 | In the kappa-deformation procedure applied to quantum free fields we should replace the classical space-time coordinates by their noncommutative counterpart and deform as well the field oscillators algebra. We introduce the kappa-deformed algebras of oscillators which are consistent with non-Abelian Hopf-algebraic kappa-deformed addition law of four-momenta. Two ways of introducing the kappa-deformed quantum fields is proposed, by
postulating for the field quanta two different types of energy-momentum dispersion relations. We describe large class of kappa-
oscillators providing the kappa-deformed free quantum fields with c-number field commutators. We present the realizations of kappa-deformed oscillator algebra in kappa-deformed Fock space, with specific energy entanglement of the kappa-deformed n-particle states. Finally we point out the role of kappa-deformed flip operator.
The results were obtained together with Marcin Daszkiewicz and Mariusz Woronowicz.
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[link as http://www.mat.uniroma2.it/08QSTNG/Lukierski]
The Schwarzschild metric in the Cartan Formalism (John Madore)
 | Spherical symmetry is discussed
within the context of a proposed noncommutative generalisation of the Cartan moving-frame formalism
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[link as http://www.mat.uniroma2.it/08QSTNG/Madore]
Models of Quantum Spacetime and Field theory. (Gherardo Piacitelli)
 | We will review the covariant approach to quantisation of the flat
Minkowski coordinates, describing the basic DFR model as well as some
modified models with non central commutators. Next, we will present some
inequivalent, noncommutative generalisations of the perturbative
approach to the quantum theory of fields, with emphasis on the open
problems and the sources of difficulties.
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[link as http://www.mat.uniroma2.it/08QSTNG/Piacitelli]
Background independence and asymptotic safety in Quantum
Einstein Gravity (Martin Reuter)
 | We review some basic concepts of the asymptotic safety
approach to quantum gravity and its implementation in terms
of the effective average action, with an emphasis on its
background independence. As any consistent theory of quantum
gravity is supposed to explain rather than postulate
spacetime, the requirement of background independence is the
crucial difference between matter quantum field theories and
gravity. By means of a simple example we demonstrate that
the background independent quantization of Einstein gravity
leads to a RG flow which differs significantly from the one
obtained on a rigid background. In particular, background
independence seems to be essential for asymptotic safety.
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[link as http://www.mat.uniroma2.it/08QSTNG/Reuter]
The vertex amplitude in quantum gravity (Carlo Rovelli)
 | I review recent developments in the loop approach to quantum gravity. I focus on the definition of the vertex amplitude. The vertex amplitude: i) codes the dynamics of the theory in a simple form; ii) is the starting point for computing n-point functions; and iii) relates the covariant *spinfoam* formalism with the hamiltonian *loop* language, providing the basis of a general language for describing the dynamics of a background-independent quantum field theory.
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[link as http://www.mat.uniroma2.it/08QSTNG/Rovelli]
 | Higher-Spin gauge theories are an enticing and little explored corner of Field Theory, and play a deep role in String Theory, whose massive excitations are mostly of this type. I shall address some long-recognized difficulties with these fields and some definite progress in their formulation that has been attained during the last years.
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[link as http://www.mat.uniroma2.it/08QSTNG/Sagnotti]
Dynamical noncommutative spaces, matrix models and gravity (Harold Steinacker)
 | A mechanism for gravity emerging from Yang-Mills matrix models is exhibited. The matrix model describes generic noncommutative spaces, which in the semi classical limit acquire an effective metric depending on the dynamical Poisson structure and the embedding metric. This leads to an emergent gravity intimately related to noncommutativity, absorbing the would-be U(1) gauge fields. The induced gravitational action captures the UV-IR mixing of NC gauge theory. Nontrivially embedded NC branes arise naturally, and are motivated by the Newtonian limit. The quantization is discussed qualitatively, which singles out the IKKT model as prime candidate for a quantum theory of gravity coupled to matter. A mechanism for avoiding the cosmological constant problem is identified.
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[link as http://www.mat.uniroma2.it/08QSTNG/Steinacker]
(Canonical) Loop Quantum Gravity (LQG) (Thomas Thiemann)
 | (Canonical) Loop Quantum Gravity (LQG) is a manifestly background independent approach to a possible synthesis of the principles of General Relativity and Quantum Field Theory. An overview over concepts, methods and results will be presented.
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[link as http://www.mat.uniroma2.it/08QSTNG/Thiemann]
Pondering over Symmetries in NC QFT and What They Lead to (Anca Tureanu)
 | The underlying symmetries of noncommutative field theories together with their implications are
analyzed. In particular, the concept of a noncommutative field based on the interplay between
twisted Poincare symmetry and residual symmetry of the Lorentz group is formulated. Various
general dynamical arguments supporting this construction, such as the light-wedge causality
condition and the integrability condition for Tomonaga-Schwinger equation, are presented. As a
byproduct, the identity between commutative QFT and noncommutative QFT with twisted Poincare
symmetry is refuted.
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[link as http://www.mat.uniroma2.it/08QSTNG/Tureanu]
Dirac field on Moyal-Minkowski spacetime and non-commutative
potential scattering (Rainer Verch)
 | We give a very rough sketch of Moyal-Minkowski spacetime (with commutative time) as a model of a Lorentzian spectral geometry. Then the quantized Dirac field will be considered on Moyal-Minkowski spacetime in that framework. Scattering of the Dirac field by a non-commutative scalar potential will be considered and it will be shown that the corresponding Bogoliubov transformation is implementable in the canonical vacuum representation of the Dirac field. Functional differentiation of the corresponding S-matrix with respect to the potential strength yields, in the spirit of Bogoliubov formula, field operators labelled by elements of the non-commutative algebra describing the Lorentzian spectral geometry of Moyal-Minkowski spacetime. By analogy with the classical case (usual Minkowski spacetime), these field operators correspond to the observable of "absolute square of field strength". The results have been obtained in collaboration with M. Borris.
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[link as http://www.mat.uniroma2.it/08QSTNG/Verch]
Heisenberg double and other crossed products (Stanislaw Woronowicz)
 | Any locally compact quantum group G=(A,Delta) comes from a manageable multiplicative unitary W. The same W gives rise to the dual group G^=(A^,Delta^). The C*-algebras A and A^ act on the same Hilbert space. By definition Heisenberg double is the norm closed linear span of {a^a: a^ in A^, a in A}. The Heisenberg double is a C*-algebra. In general it depends on the choice of W, however it is possible to find an universal W producing the largest possible Heisenberg double. Heisenberg double is an example of a crossed product of C*-algebras. We shall introduce a general notion of the crossed product and discuss some examples.
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[link as http://www.mat.uniroma2.it/08QSTNG/Woronowicz]
Non-compact spectral triples with finite volume (Raimar Wulkenhaar)
 | In order to extend the spectral action principle to non-compact spaces, I propose a framework for spectral triples where the algebra may be non-unital but the resolvent of the Dirac operator remains compact. I show that an example is given by the commutative Schwartz algebra together with the Dirac operator of the harmonic oscillator.
I also compute the spectral action for the corresponding Connes-Lott two-point model. There is an additional harmonic oscillator potential for the Higgs field, whereas the Yang-Mills part is unchanged. The total Higgs potential shows a two-phase structure with smooth transition between them: In the spontaneously broken phase below a critical radius, all fields are massive, with the Higgs mass slightly smaller than the NCG prediction. In the unbroken phase above the critical radius, gauge fields and fermions are massless, whereas the Higgs remains massive. The masses of gauge fields and fermions dissipate into the cosmological constant.
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[link as http://www.mat.uniroma2.it/08QSTNG/Wulkenhaar]
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