arXiv subjects

Annalisa Marzuoli

Publications and source records attributed to Annalisa Marzuoli.

25 records · Page 2Linked to original sources

arXiv2004

Spin network setting of topological quantum computation

The spin network simulator model represents a bridge between (generalised) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFTs). The key tool is provided by the fiber space structure underlying the model which exhibits combinatorial properties closely related to SU(2) state sum models, widely employed in discretizing TQFTs and quantum gravity in low spacetime dimensions.

quant-ph↗

arXiv2003

Conformal modes in simplicial quantum gravity and the Weil-Petersson volume of moduli space

Our goal here is to present a detailed analysis connecting the anomalous scaling properties of 2D simplicial quantum gravity to the geometry of the moduli space M_{g,N} of genus g Riemann surfaces with N punctures. In the case of pure gravity we prove that the scaling properties of the set of dynamical triangulations with N vertices are directly provided by the large N asymptotics of the Weil-Petersson volume of M_{g,N}, recently discussed by Manin and Zograf. Such a geometrical characterization explains why dynamical triangulations automatically take into account the anomalous scaling properties of Liouville theory. In the case of coupling with conformal matter we briefly argue that the anomalous scaling of the resulting discretized theory should be related to the Gromov-Witten invariants of the moduli space M_{g,N}(X,β) of stable maps from (punctured Riemann surfaces associated with) dynamical triangulations to a manifold X parameterizing the conformal matter configurations.

math-ph↗

arXiv2002

Spin network quantum simulator

We propose a general setting for a universal representation of the quantum structure on which quantum information stands, whose dynamical evolution (information manipulation) is based on angular momentum recoupling theory. Such scheme complies with the notion of 'quantum simulator' in the sense of Feynmann, and is shown to be related with the topological quantum field theory approach to quantum computation.

quant-ph↗

arXiv2000

Hierarchies of invariant spin models

In this paper we present classes of state sum models based on the recoupling theory of angular momenta of SU(2) (and of its q-counterpart $U_q(sl(2))$, q a root of unity). Such classes are arranged in hierarchies depending on the dimension d, and include all known closed models, i.e. the Ponzano-Regge state sum and the Turaev-Viro invariant in dimension d=3, the Crane-Yetter invariant in d=4. In general, the recoupling coefficient associated with a d-simplex turns out to be a $\{3(d-2)(d+1)/2\}j$ symbol, or its q-analog. Each of the state sums can be further extended to compact triangulations $(T^d,\partial T^d)$ of a PL-pair $(M^d,\partial M^d)$, where the triangulation of the boundary manifold is not keeped fixed. In both cases we find out the algebraic identities which translate complete sets of topological moves, thus showing that all state sums are actually independent of the particular triangulation chosen. Then, owing to Pachner's theorems, it turns out that classes of PL-invariant models can be defined in any dimension d.

gr-qc↗

arXiv2000

Moduli space intersection duality between Regge surfaces and 2D dynamical triangulations

Deformation theory for 2-dimensional dynamical triangulations with N vertices is discussed by exploiting the geometry of the moduli space of Euclidean polygons. Such an analysis provides an explicit connection among Regge surfaces, dynamical triangulations and the Witten-Kontsevich model. We show that a natural set of Regge measures and a triangulation counting of relevance for dynamical triangulations are directly connected with intersection theory over the compactified moduli space of genus g Riemann surfaces with N punctures.The Regge measures in question provide volumes of the open strata in moduli space. It is also argued that the arguments presented here offer evidence of a form of topological S-duality between Regge calculus and DT theory.

math-ph↗

arXiv1999

Invariants of spin networks with boundary in Quantum Gravity and TQFT's

The search for classical or quantum combinatorial invariants of compact n-dimensional manifolds (n=3,4) plays a key role both in topological field theories and in lattice quantum gravity. We present here a generalization of the partition function proposed by Ponzano and Regge to the case of a compact 3-dimensional simplicial pair $(M^3, \partial M^3)$. The resulting state sum $Z[(M^3, \partial M^3)]$ contains both Racah-Wigner 6j symbols associated with tetrahedra and Wigner 3jm symbols associated with triangular faces lying in $\partial M^3$. The analysis of the algebraic identities associated with the combinatorial transformations involved in the proof of the topological invariance makes it manifest a common structure underlying the 3-dimensional models with empty and non empty boundaries respectively. The techniques developed in the 3-dimensional case can be further extended in order to deal with combinatorial models in n=2,4 and possibly to establish a hierarchy among such models. As an example we derive here a 2-dimensional closed state sum model including suitable sums of products of double 3jm symbols, each one of them being associated with a triangle in the surface.

gr-qc↗

arXiv1992

12j-symbols and four-dimensional quantum gravity

We propose a model which represents a four-dimensional version of Ponzano and Regge's three-dimensional euclidean quantum gravity. In particular we show that the exponential of the euclidean Einstein-Regge action for a $4d$-discretized block is given, in the semiclassical limit, by a gaussian integral of a suitable $12j$-symbol. Possible developments of this result are discussed.

hep-th↗