Related papers: A New Recursion Relation for the 6j-Symbol
A comparative study of the magnetic properties of shunted and unshunted two-dimensional Josephson junction arrays (2D-JJA) is presented. Using a single-plaquette approximation of the 2D-JJA model, we were able to successfully fit all our…
The ZX-calculus, and the variant we consider in this paper (ZXH-calculus), are formal diagrammatic languages for qubit quantum computing. We show that it can also be used to describe SU(2) representation theory. To achieve this, we first…
We propose a recursion relation for tree-level scattering amplitudes in three-dimensional Chern-Simons-matter theories. The recursion relation involves a complex deformation of momenta which generalizes the BCFW-deformation used in higher…
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…
The Clebsch-Gordan coefficients or Wigner $3j$ symbols are known to be proportional to a $_3F_2(1)$ hypergeometric series, and Racah $6j$ coefficients to a $_4F_3(1)$. In general, however, non-trivial $9j$ symbols can not be expressed as a…
The definition of the Ponzano-Regge state-sum model of three-dimensional quantum gravity with a class of local observables is developed. The main definition of the Ponzano-Regge model in this paper is determined by its reformulation in…
A consequence of the surgery theorem of Gromov and Lawson is that every closed, simply-connected 6-manifold admits a Riemannian metric of positive scalar curvature. For metrics of positive Ricci curvature it is widely open whether a similar…
Let A, B denote generic binary forms, and let u_r = (A,B)_r denote their r-th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the u_r. As a consequence, we show that each…
We present a geometrical formulation of nonlinear electrodynamics by expressing its principal symbol as an optical metric-induced object. Under the assumption of no birefringence, we show that the evolution of linear perturbations can be…
We consider the dynamics of the Sorkin-Johnston (SJ) state for a massless scalar field in two dimensions. We conduct a study of the renormalized stress-tensor by a subtraction procedure, and compare the results with those of the conformal…
We show that 3D gravity, in its pure connection formulation, admits a natural 6D interpretation. The 3D field equations for the connection are equivalent to 6D Hitchin equations for the Chern-Simons 3-form in the total space of the…
An alternative approach introducing a 3 dimensional Ricci scalar curvature quantum operator given in terms of volume and area as well as new edge length operators is proposed. An example of monochromatic 4-valent node intertwiner state…
In this work, we present a recurrence relation for the instanton partition function of the $\mathcal{N}=2$ SYM $SU(N)$ gauge theory with $2N$ fundamental multiplets. The main difficulty lies in determining the asymptotic behaviour of the…
Using the tools of q--differential calculus and quantum Lie algebras associated to quantum groups, we find a one--parameter family of q-gauge theories associated to the quantum group $ISO_q(3,1)$. Although the gauge fields, that is the…
The massive six-dimensional (6D) superparticle with manifest (n,0) supersymmetry is shown to have a supertwistor formulation in which its "hidden" (0,n) supersymmetry is also manifest. The mass-shell constraint is replaced by Spin(5)…
In this paper, a candidate for pregeometry, Ponzano-Regge spin networks, will be examined in the context of the pregeometric philosophy of Wheeler. Ponzano and Regge were able to construct a theory for 3-dimensional quantum gravity based on…
In a previous work we considered the number of pairs of particles with angular momentum J12 for systems with angular momentum zero.Here we extend the work to states of any total angular momentum.We find simplified relations satisfied for a…
We show how the expectation values of geometrical quantities in 3d quantum gravity can be explicitly computed using grasping rules. We compute the volume of a labelled tetrahedron using the triple grasping. We show that the large spin…
The use of orthogonal polynomials for integral models on the lattice is applied to the 3nj-symbols that appear in the coupling of several angular momenta. These symbols are connected to the Ponzano-Regge method to solve the Einstein…
Many iterative methods in applied mathematics can be thought of as fixed-point iterations, and such algorithms are usually analyzed analytically, with inequalities. In this paper, we present a geometric approach to analyzing contractive and…