Related papers: Deriving identities for Wigner {nj}-symbols
In this paper we derive a differential identity for linearized gravity on the Kerr spacetime and more generally on vacuum spacetimes of Petrov type D. We show that a linear combination of second derivatives of the linearized Weyl tensor can…
There are two types of asymptotic formulas for the $12j$ symbol with one small and 11 large angular momenta. We have derived the first type of formula previously in [L. Yu, Phys. Rev. A84 022101 (2011)]. We will derive the second type in…
The Schl\"afli identity, which is important in Regge calculus and loop quantum gravity, is examined from a symplectic and semiclassical standpoint in the special case of flat, 3-dimensional space. In this case a proof is given, based on…
This paper investigates the relation between colored HOMFLY-PT and Kauffman homology, $\text{SO}(N)$ quantum $6j$-symbols and $(a,t)$-deformed $F_K$. First, we present a simple rule of grading change which allows us to obtain the…
Dodgson polynomials appear in Schwinger parametric Feynman integrals and are closely related to the well known Kirchhoff (or first Symanzik) polynomial. In this article a new combinatorial interpretation and a generalisation of Dodgson…
Dendriform structures arise naturally in algebraic combinatorics (where they allow, for example, the splitting of the shuffle product into two pieces) and through Rota-Baxter algebra structures (the latter appear, among others, in…
We prove new determinantal identities for a family of flagged Schur polynomials. As a corollary of these identities we obtain determinantal expressions of Schubert polynomials for certain vexillary permutations.
Starting from basic identities of the group E8, we perform progressive reductions, namely decompositions with respect to the maximal and symmetric embeddings of E7xSU(2) and then of E6xU(1). This procedure provides a systematic approach to…
We present a set of bilinear matrix identities that generalize the ones that have been used to construct the bright soliton solutions for various models. As an example of an application of these identities, we present a simple derivation of…
In this paper, we rewrite two forms of an Euler-Ramanujan identity in terms of certain Dirichlet series and derive functional equation of the latter. We also use the Weierstrass-Enneper representation of minimal surfaces to obtain some…
We prove a new identity for Feynman periods that acts on five-vertex cuts of completed primitive Feynman graphs. It is shown that in $\phi^4$ theory this identity is independent from existing identities which are the twist, the Fourier…
We present new soft theorems for photon, gluon, and graviton correlators at tree level in (Anti)-de Sitter space. The results are derived by applying conformal Ward identities to constrain the structure of Witten diagrams.
In split or Kleinian signature, twistor constructions parametrize solutions to both gauge and gravity self-duality (SD) equation from twistor data that can be expressed in terms of free smooth data without gauge freedom. Here the…
We discuss the dynamic properties of the square-lattice spin-1/2 XY model obtained using the two-dimensional Jordan-Wigner fermionization approach. We argue the relevancy of the fermionic picture for interpreting the neutron scattering…
We adapt the Gurau's proof (2008) about the asymptotic limit of Ponzano-Regge formula to supersymmetric 6jS symbols according to their intrinsic parities alpha, beta, gamma. The behaviour at a large scaling shows significant differences…
We revisit the 5D gravity model by Dvali, Gabadadze, and Porrati (DGP). Within their framework it was shown that even in 5D non-compact Minkowski space $(x^\mu,z)$, the Newtonian gravity can emerge on a brane at short distances by…
We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral given by an integral over suitable…
We derive new identities involving zeros of the Bessel function $J_{\nu}$ and some related functions. These are special cases of more general identities obtained in this note, which might also be of interest.
In this paper we express some simple random tensor models in a Givental-like fashion i.e. as differential operators acting on a product of generic 1-Hermitian matrix models. Finally we derive Hirota's equations for these tensor models. Our…
We derive several identities that feature irreducible characters of the general linear, the symplectic, the orthogonal, and the special orthogonal groups. All the identities feature characters that are indexed by shapes that are "nearly"…