Related papers: Asymptotics of LQG fusion coefficients
Spin foam models for quantum gravity are derived from lattice path integrals. The setting involves variables from both lattice BF theory and Regge calculus. The action consists in a Regge action, which depends on areas, dihedral angles and…
We study electron spin decoherence in a two-electron double quantum dot due to the hyperfine interaction, under spin-echo conditions as studied in recent experiments. We develop a semi-classical model for the interaction between the…
The goal of this paper is to introduce a systematic approach to spin foams. We define operator spin foams, that is foams labelled by group representations and operators, as the main tool. An equivalence relation we impose in the set of the…
We apply the semi-classical limit of the generalized $SO(3)$ map for representation of variable-spin systems in a four-dimensional symplectic manifold and approximate their evolution terms of effective classical dynamics on $T^{\ast…
We analyze the large-spin asymptotics of a class of spin-network wavefunctions of Euclidean Loop Quantum Gravity, which corresponds to a flat spacetime. A wavefunction from this class can be represented as a sum over the spins of an…
Unlike that of SO(3) or SU(2), the Lie algebra for SO(2), which defines intermediate spin, comprises only $S_{z}$ and implies $S^{\pm}$ commute. In general, $S_{z}$ has a continuous spectrum. This intermediate spin scheme can realized for…
In part I of [1] we have developed the tensor and spin representation of SO(4) in order to apply it to the simplicial decomposition of the Barrett-Crane model. We attach to each face of a triangle the spherical function constructed from the…
The two-channel Anderson lattice model which has $SU(2)\otimes SU(2)$ symmetry is of relevance to understanding of the magnetic, quadrupolar and superconducting phases in U$_{1-x}$Th$_x$Be$_{13}$ or Pr base skutterudite compounds such as…
This thesis is developed in the context of the spin-foam approach to quantum gravity; all results are concerned with the Lorentzian theory and with semiclassical methods. A correspondence is given between Majorana 2-spinors and time-like…
We study a model of N-component complex fermions with a kinetic term that is second order in derivatives. This symplectic fermion model has an Sp(2N) symmetry, which for any N contains an SO(3) subgroup that can be identified with…
A SU(2) intertwiner with N legs can be interpreted as the quantum state of a convex polyhedron with N faces (when working in 3d). We show that the intertwiner Hilbert space carries a representation of the non-compact group SO*(2N). This…
The 7--particle form factors of the fundamental spin field of the O(3) nonlinear $\sigma$--model are constructed. We calculate the corresponding contribution to the spin--spin correlation function, and compare with predictions from the…
The observed deep inelastic nucleon spin asymmetries $A_{1}^{p,n}$ and the spin dependent quark distributions break SU(6) spin - flavour symmetry. In quark models two mechanisms for breaking SU(6) symmetry are well known: the hyperfine…
We investigate the group field theory formulation of the EPRL/FK spin foam models. These models aim at a dynamical, i.e. non-topological formulation of 4D quantum gravity. We introduce a saddle point method for general group field theory…
We study the large-j asymptotics of the Euclidean EPRL/FK spin foam amplitude on a 4d simplicial complex with arbitrary number of simplices. We show that for a critical configuration (j_f, g_{ve}, n_{ef}) in general, there exists a…
We present a practical semiclassical method for computing the electron spin dynamics of a radical in which the electron spin is hyperfine coupled to a large number of nuclear spins. This can be used to calculate the singlet and triplet…
The group $PGL(2,q)$ has an embedding into $PGL(3,q)$ such that it acts as the group fixing a nonsingular conic in $PG(2,q)$. This action affords a coherent configuration $R(q)$ on the set $L(q)$ of non-tangent lines of the conic. We show…
A specific new quark permits that flavor generations constitute a representation of the 3-dimensional SU(3) symmetry that characterizes the Z(3) orbifold. In this context, color and supergravity bind triplets and 4-tuplets into composite…
We theoretically consider coherence times for spins in two quantum computer architectures, where the qubit is the spin of an electron bound to a P donor impurity in Si or within a GaAs quantum dot. We show that low temperature decoherence…
We study the asymptotic geometry of the spin foam partition function for a large class of models, including the models of Barrett and Crane, Engle, Pereira, Rovelli and Livine, and, Freidel and Krasnov. The asymptotics is taken with respect…