172 research outputs found
Forecasting of the Possible Outcome of Prosthetics of the Aortal Valve on Preoperational Anatomo-Functional Hemodynamics and According to Heart Indicators
Topological Quantum Field Theories and Operator Algebras
We review "quantum" invariants of closed oriented 3-dimensional manifolds
arising from operator algebras.Comment: For proceedings of "International Workshop on Quantum Field Theory
and Noncommutative Geometry", Sendai, November 200
Some computations in the cyclic permutations of completely rational nets
In this paper we calculate certain chiral quantities from the cyclic
permutation orbifold of a general completely rational net. We determine the
fusion of a fundamental soliton, and by suitably modified arguments of A. Coste
, T. Gannon and especially P. Bantay to our setting we are able to prove a
number of arithmetic properties including congruence subgroup properties for
matrices of a completely rational net defined by K.-H. Rehren .Comment: 30 Pages Late
A matrix solution to pentagon equation with anticommuting variables
We construct a solution to pentagon equation with anticommuting variables
living on two-dimensional faces of tetrahedra. In this solution, matrix
coordinates are ascribed to tetrahedron vertices. As matrix multiplication is
noncommutative, this provides a "more quantum" topological field theory than in
our previous works
Quantum Gravity, Dynamical Triangulation and Higer Derivative Regularization
We consider a discrete model of euclidean quantum gravity in four dimensions
based on a summation over random simplicial manifolds. The action used is the
Einstein-Hilbert action plus an -term. The phase diagram as a function of
the bare coupling constants is studied in the search for a sensible continuum
limit. For small values of the coupling constant of the term the model
seems to belong to the same universality class as the model with pure
Einstein-Hilbert action and exhibits the same phase transition. The order of
the transition may be second or higher. The average curvature is positive at
the phase transition, which makes it difficult to understand the possible
scaling relations of the model.Comment: 27 pages (Latex), figures not included. Post script file containing
15 figures (1000 blocks) available from [email protected]
Spacetime as a Feynman diagram: the connection formulation
Spin foam models are the path integral counterparts to loop quantized
canonical theories. In the last few years several spin foam models of gravity
have been proposed, most of which live on finite simplicial lattice spacetime.
The lattice truncates the presumably infinite set of gravitational degrees of
freedom down to a finite set. Models that can accomodate an infinite set of
degrees of freedom and that are independent of any background simplicial
structure, or indeed any a priori spacetime topology, can be obtained from the
lattice models by summing them over all lattice spacetimes. Here we show that
this sum can be realized as the sum over Feynman diagrams of a quantum field
theory living on a suitable group manifold, with each Feynman diagram defining
a particular lattice spacetime. We give an explicit formula for the action of
the field theory corresponding to any given spin foam model in a wide class
which includes several gravity models. Such a field theory was recently found
for a particular gravity model [De Pietri et al, hep-th/9907154]. Our work
generalizes this result as well as Boulatov's and Ooguri's models of three and
four dimensional topological field theories, and ultimately the old matrix
models of two dimensional systems with dynamical topology. A first version of
our result has appeared in a companion paper [gr-qc\0002083]: here we present a
new and more detailed derivation based on the connection formulation of the
spin foam models.Comment: 32 pages, 2 figure
Colored Group Field Theory
Group field theories are higher dimensional generalizations of matrix models.
Their Feynman graphs are fat and in addition to vertices, edges and faces, they
also contain higher dimensional cells, called bubbles. In this paper, we
propose a new, fermionic Group Field Theory, posessing a color symmetry, and
take the first steps in a systematic study of the topological properties of its
graphs. Unlike its bosonic counterpart, the bubbles of the Feynman graphs of
this theory are well defined and readily identified. We prove that this graphs
are combinatorial cellular complexes. We define and study the cellular homology
of this graphs. Furthermore we define a homotopy transformation appropriate to
this graphs. Finally, the amplitude of the Feynman graphs is shown to be
related to the fundamental group of the cellular complex
Quantum geometry from 2+1 AdS quantum gravity on the torus
Wilson observables for 2+1 quantum gravity with negative cosmological
constant, when the spatial manifold is a torus, exhibit several novel features:
signed area phases relate the observables assigned to homotopic loops, and
their commutators describe loop intersections, with properties that are not yet
fully understood. We describe progress in our study of this bracket, which can
be interpreted as a q-deformed Goldman bracket, and provide a geometrical
interpretation in terms of a quantum version of Pick's formula for the area of
a polygon with integer vertices.Comment: 19 pages, 11 figures, revised with more explanations, improved
figures and extra figures. To appear GER
Quantum Gravity and the Algebra of Tangles
In Rovelli and Smolin's loop representation of nonperturbative quantum
gravity in 4 dimensions, there is a space of solutions to the Hamiltonian
constraint having as a basis isotopy classes of links in R^3. The physically
correct inner product on this space of states is not yet known, or in other
words, the *-algebra structure of the algebra of observables has not been
determined. In order to approach this problem, we consider a larger space H of
solutions of the Hamiltonian constraint, which has as a basis isotopy classes
of tangles. A certain algebra T, the ``tangle algebra,'' acts as operators on
H. The ``empty state'', corresponding to the class of the empty tangle, is
conjectured to be a cyclic vector for T. We construct simpler representations
of T as quotients of H by the skein relations for the HOMFLY polynomial, and
calculate a *-algebra structure for T using these representations. We use this
to determine the inner product of certain states of quantum gravity associated
to the Jones polynomial (or more precisely, Kauffman bracket).Comment: 16 pages (with major corrections
Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
Many trial wavefunctions for fractional quantum Hall states in a single
Landau level are given by functions called conformal blocks, taken from some
conformal field theory. Also, wavefunctions for certain paired states of
fermions in two dimensions, such as p_x+ip_y states, reduce to such a form at
long distances. Here we investigate the adiabatic transport of such
many-particle trial wavefunctions using methods from two-dimensional field
theory. One context for this is to calculate the statistics of widely-separated
quasiholes, which has been predicted to be non-Abelian in a variety of cases.
The Berry phase or matrix (holonomy) resulting from adiabatic transport around
a closed loop in parameter space is the same as the effect of analytic
continuation around the same loop with the particle coordinates held fixed
(monodromy), provided the trial functions are orthonormal and holomorphic in
the parameters so that the Berry vector potential (or connection) vanishes. We
show that this is the case (up to a simple area term) for paired states
(including the Moore-Read quantum Hall state), and present general conditions
for it to hold for other trial states (such as the Read-Rezayi series). We
argue that trial states based on a non-unitary conformal field theory do not
describe a gapped topological phase, at least in many cases. By considering
adiabatic variation of the aspect ratio of the torus, we calculate the Hall
viscosity, a non-dissipative viscosity coefficient analogous to Hall
conductivity, for paired states, Laughlin states, and more general quantum Hall
states. Hall viscosity is an invariant within a topological phase, and is
generally proportional to the "conformal spin density" in the ground state.Comment: 44 pages, RevTeX; v2 minor changes; v3 typos corrected, three small
addition
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