Recursion Relation for Wick Products of the CCR Algebra

2008 ◽  
Vol 2 (3) ◽  
pp. 441-447 ◽  
Author(s):  
Benito J. González ◽  
Emilio R. Negrin
Keyword(s):  
Recursion Relation ◽  
Ccr Algebra ◽  
Wick Products

Wick products of the CCR algebra

2011 ◽  
Vol 284 (10) ◽  
pp. 1280-1285
Author(s):  
B. J. González ◽  
E. R. Negrin
Keyword(s):  
Ccr Algebra ◽  
Wick Products

scholarly journals Notes on gravity multiplet correlators in AdS3 × S3

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Congkao Wen ◽  
Shun-Qing Zhang
Keyword(s):  
Recursion Relation ◽  
Conformal Symmetry ◽  
Flat Space ◽  
The Other ◽  
Tree Level ◽  
Space Limit ◽  
Compact Expression ◽  
Tensor Multiplet ◽  
R Symmetry

Abstract We present a compact formula in Mellin space for the four-point tree-level holographic correlators of chiral primary operators of arbitrary conformal weights in (2, 0) supergravity on AdS3× S3, with two operators in tensor multiplet and the other two in gravity multiplet. This is achieved by solving the recursion relation arising from a hidden six-dimensional conformal symmetry. We note the compact expression is obtained after carefully analysing the analytic structures of the correlators. Various limits of the correlators are studied, including the maximally R-symmetry violating limit and flat-space limit.

scholarly journals RECURSION FOR MASUR-VEECH VOLUMES OF MODULI SPACES OF QUADRATIC DIFFERENTIALS

2021 ◽  
pp. 1-6
Author(s):  
Maxim Kazarian
Keyword(s):  
Moduli Spaces ◽  
Recursion Relation ◽  
Quadratic Differentials ◽  
Hodge Integrals

Abstract We derive a quadratic recursion relation for the linear Hodge integrals of the form $\langle \tau _{2}^{n}\lambda _{k}\rangle $ . These numbers are used in a formula for Masur-Veech volumes of moduli spaces of quadratic differentials discovered by Chen, Möller and Sauvaget. Therefore, our recursion provides an efficient way of computing these volumes.

scholarly journals THE CRITICAL POINT OF UNORIENTED RANDOM SURFACES WITH A NONEVEN POTENTIAL

1993 ◽  
Vol 08 (06) ◽  
pp. 1139-1152
Author(s):  
M.A. MARTÍN-DELGADO
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Critical Point ◽  
Discrete Model ◽  
Recursion Relation ◽  
Scaling Limit ◽  
Random Surfaces ◽  
Matrix Ensemble ◽  
Quartic Interaction ◽  
Double Scaling Limit

The discrete model of the real symmetric one-matrix ensemble is analyzed with a cubic interaction. The partition function is found to satisfy a recursion relation that solves the model. The double scaling-limit of the recursion relation leads to a Miura transformation relating the contributions to the free energy coming from oriented and unoriented random surfaces. This transformation is the same kind as found with a quartic interaction.

scholarly journals THE NON-COMMUTATIVE A-POLYNOMIAL OF TWIST KNOTS

2010 ◽  
Vol 19 (12) ◽  
pp. 1571-1595 ◽  
Author(s):  
STAVROS GAROUFALIDIS ◽  
XINYU SUN
Keyword(s):  
Difference Equation ◽  
Recursion Relation ◽  
Jones Polynomial ◽  
Minimal Order ◽  
Quantum Topology ◽  
And Topology ◽  
Jones Polynomials ◽  
Creative Telescoping ◽  
Colored Jones Polynomials ◽  
Telescoping Method

The purpose of the paper is two-fold: to introduce a multivariable creative telescoping method, and to apply it in a problem of Quantum Topology: namely the computation of the non-commutative A-polynomial of twist knots. Our multivariable creative telescoping method allows us to compute linear recursions for sums of the form [Formula: see text] given a recursion relation for [Formula: see text] and the hypergeometric kernel c(n, k). As an application of our method, we explicitly compute the non-commutative A-polynomial for twist knots with -15 and 15 crossings. The non-commutative A-polynomial of a knot encodes the monic, linear, minimal order q-difference equation satisfied by the sequence of colored Jones polynomials of the knot. Its specialization to q = 1 is conjectured to be the better-known A-polynomial of a knot, which encodes important information about the geometry and topology of the knot complement. Unlike the case of the Jones polynomial, which is easily computable for knots with 50 crossings, the A-polynomial is harder to compute and already unknown for some knots with 12 crossings.

scholarly journals Bound states of an inverse-cube singular potential: A candidate for electron-quadrupole binding

2019 ◽  
Vol 34 (28) ◽  
pp. 1950223 ◽  
Author(s):  
A. D. Alhaidari
Keyword(s):  
Bound States ◽  
Recursion Relation ◽  
Singular Potential ◽  
Electric Quadrupole ◽  
Exact Bound ◽  
Short Range Potential ◽  
Integrable Functions ◽  
Solution Energy ◽  
Expansion Coefficients ◽  
Square Integrable Functions

We use the Tridiagonal Representation Approach (TRA) to obtain exact bound states solution (energy spectrum and wave function) of the Schrödinger equation for a three-parameter short-range potential with [Formula: see text], [Formula: see text] and [Formula: see text] singularities at the origin. The solution is a finite series of square-integrable functions with expansion coefficients that satisfy a three-term recursion relation. The solution of the recursion is a non-conventional orthogonal polynomial with discrete spectrum. The results of this work could be used to study the binding of an electron to a molecule with an effective electric quadrupole moment which has the same [Formula: see text] singularity.

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