Related papers: Generating Functions for Coherent Intertwiners
A gauge invariant Hamiltonian representation for SU(2) in terms of a spin network basis is introduced. The vectors of the spin network basis are independent and the electric part of the Hamiltonian is diagonal in this representation. The…
It is observed that the conjugacy growth series of the infinite fini-tary symmetric group with respect to the generating set of transpositions is the generating series of the partition function. Other conjugacy growth series are computed,…
We obtain the hole propagator of the Sutherland model with SU(2) internal symmetry for coupling parameter $\beta=1$, which is the simplest nontrivial case. One created hole with spin down breaks into two quasiholes with spin down and one…
We present a self-consistent theoretical framework for finite-dimensional discrete phase spaces that leads us to establish a well-grounded mapping scheme between Schwinger unitary operators and generators of the special unitary group…
We show that, for SU(2) generators of arbitrary dimension $D$, there exist identities that express the completely symmetric product of $D$ matrices in terms of completely symmetric products of fewer number of matrices. We also indicate why…
Spinor-vector dualities have been established in various exact string realisations like orbifold and free fermionic constructions. This paper aims to investigate possibility of having spinor-vector dualities on smooth geometries in the…
We compute, by free field techniques, the scalar product of the SU(2) Chern-Simons states on genus > 1 surfaces. The result is a finite-dimensional integral over positions of ``screening charges'' and one complex modular parameter. It uses…
We study a generating function for the sum over fatgraphs with specified valences of vertices and faces, inversely weighted by the order of their symmetry group. A compact expression is found for general (i.e. non necessarily connected)…
As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…
Duality in the integrable systems arising in the context of Seiberg-Witten theory shows that their tau-functions indeed can be seen as generating functions for the mutually Poisson-commuting hamiltonians of the {\em dual} systems. We…
The inclusion of a flat metric tensor in gravitation permits the formulation of a gravitational stress-energy tensor and the formal derivation of general relativity from a linear theory in flat spacetime. Building on the works of Kraichnan…
The whole enterprise of spin compositions can be recast as simple enumerative combinatoric problems. We show here that enumerative combinatorics (EC)\citep{book:Stanley-2011} is a natural setting for spin composition, and easily leads to…
Tensor products of standard model bosons and fermions form a spin-2 self-realization of SU(5), and because every quark can be interpreted as a lepton that has coupled to an appropriate element of this adjoint representation, and inversely,…
We formulate the spin foam representation of discrete SU(2) gauge theory as a product of vertex amplitudes each of which is the spin network generating function of the boundary graph dual to the vertex. In doing so the sums over spins have…
One of the most challenging hurdles to the construction of realistic composite Higgs models is the generation of Yukawa couplings for the Standard Model fermions. This problem can be successfully addressed in approximate conformal theories…
Using the generating function of SU(n) we find the conjugate state of SU(n) basis and we find in terms of Gel'fand basis of SU(3(n-1)) the representation of the invariants of the Kronecker products of SU(n). We find a formula for the number…
Quantum simulations of many-body systems offer novel methods for probing the dynamics of the Standard Model and its constituent gauge theories. Extracting low-energy predictions from such simulations rely on formulating…
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries…
In this paper we discuss a proposal of coherent states for Loop Quantum Gravity. These states are labeled by a point in the phase space of General Relativity as captured by a spin-network graph. They are defined as the gauge invariant…
The bilinear generating function for products of two Laguerre 2D polynomials Lm;n(z; z0) with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polynomials.…