On the S-Matrix of the Faddeev-Reshetikhin Model

Constrained dynamics of two interacting relativistic particles in the Faddeev-Jackiw symplectic framework

The Faddeev-Jackiw symplectic formalism for constrained systems is applied to analyze the dynamical content of a model describing two massive relativistic particles with interaction, which can also be interpreted as a bigravity model in one dimension. We systematically investigate the nature of the physical constraints, for which we also determine the zero-modes structure of the corresponding symplectic matrix. After identifying the whole set of constraints, we find out the transformation laws for all the set of dynamical variables corresponding to gauge symmetries, encoded in the remaining ze…

Symmetry transform in the Faddeev-Jackiw quantization of dual models

We study the presence of symmetry transformations in the Faddeev-Jackiw approach for constrained systems. Our analysis is based in the case of a particle submitted to a particular potential which depends on an arbitrary function. The method is implemented in a natural way and symmetry generators are identified. These symmetries permit us to obtain the absent elements of the sympletic matrix which complement the set of Dirac brackets of such a theory. The study developed here is applied in two different dual models. First, we discuss the case of a two-dimensional oscillator interacting with an …

The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring

We discuss the Zamolodchikov-Faddeev algebra for the superstring sigma-model on AdS_5 x S^5. We find the canonical su(2|2)^2 invariant S-matrix satisfying the standard Yang-Baxter and crossing symmetry equations. Its near-plane-wave expansion matches exactly the leading order term recently obtained by the direct perturbative computation. We also show that the S-matrix obtained by Beisert in the gauge theory framework does not satisfy the standard Yang-Baxter equation, and, as a consequence, the corresponding ZF algebra is twisted. The S-matrices in gauge and string theories however are physica…

From Faddeev-Kulish to LSZ. Towards a non-perturbative description of colliding electrons

In a low energy approximation of the massless Yukawa theory (Nelson model) we derive a Faddeev-Kulish type formula for the scattering matrix of $N$ electrons and reformulate it in LSZ terms. To this end, we perform a decomposition of the infrared finite Dollard modifier into clouds of real and virtual photons, whose infrared divergencies mutually cancel. We point out that in the original work of Faddeev and Kulish the clouds of real photons are omitted, and consequently their scattering matrix is ill-defined on the Fock space of free electrons. To support our observations, we compare our final…

Faddeev-Jackiw哈密顿形式化用于一般奇异双引力

Faddeev-Jackiw Hamiltonian formulation for general exotic bi-gravity

该研究采用辛几何方法分析一般奇异双引力理论的动力学结构，推导出全部约束与标量关系，并应用于反德西特背景，最终证明该理论具有两个物理自由度。

通过$R$-矩阵进行Bootstrap

Bootstrapping the $R$-matrix

本文提出通过代数方法求解量子自旋链$R$-矩阵的Bootstrap程序，利用Kennedy引理迭代求解$R$-矩阵系数，探讨其与Yang-Baxter方程的关联及可积性检验作用。

On a nonstandard two-parametric quantum algebra and its connections with $U_{p,q}(gl(2))$ and $U_{p,q}(gl(1|1))$

A quantum algebra $U_{p,q}(ζ,H,X_\pm )$ associated with a nonstandard $R$-matrix with two deformation parameters$(p,q)$ is studied and, in particular, its universal ${\cal R}$-matrix is derived using Reshetikhin's method. Explicit construction of the $(p,q)$-dependent nonstandard $R$-matrix is obtained through a coloured generalized boson realization of the universal ${\cal R}$-matrix of the standard $U_{p,q}(gl(2))$ corresponding to a nongeneric case. General finite dimensional coloured representation of the universal ${\cal R}$-matrix of $U_{p,q}(gl(2))$ is also derived. This representation,…

Classical and Quantum sl(1|2) Superalgebras, Casimir Operators and Quantum Chain Hamiltonians

We examine the two parameter deformed superalgebra $U_{qs}(sl(1|2))$ and use the results in the construction of quantum chain Hamiltonians. This study is done both in the framework of the Serre presentation and in the $R$-matrix scheme of Faddeev, Reshetikhin and Takhtajan (FRT). We show that there exists an infinite number of Casimir operators, indexed by integers $p > 1$ in the undeformed case and by $p \in Z$ in the deformed case, which obey quadratic relations. The construction of the dual superalgebra of functions on $SL_{qs}(1|2)$ is also given and higher tensor product representations a…

Spectral Decomposition and Baxterisation of Exotic Bialgebras and Associated Noncommutative Geometries

We study the geometric aspects of two exotic bialgebras S03 and S14 introduced in math.QA/0206053. These bialgebras are obtained by the Faddeev-Reshetikhin-Takhtajan RTT prescription with non-triangular R-matrices which are denoted $R_{03}$ and $R_{14}$ in the classification of Hietarinta, and they are not deformations of either GL(2) or GL(1/1). We give the spectral decomposition which involves two, resp., three, projectors. These projectors are then used to provide the Baxterisation procedure with one, resp., two, parameters. Further, the projectors are used to construct the noncommutative p…

Ghost Sector in Minimal Linear Covariant Gauge

We discuss possible definitions of the Faddeev-Popov matrix for the minimal linear covariant gauge on the lattice and present preliminary results for the ghost propagator.

Matrix models from operators and topological strings, 2

The quantization of mirror curves to toric Calabi--Yau threefolds leads to trace class operators, and it has been conjectured that the spectral properties of these operators provide a non-perturbative realization of topological string theory on these backgrounds. In this paper, we find an explicit form for the integral kernel of the trace class operator in the case of local P1xP1, in terms of Faddeev's quantum dilogarithm. The matrix model associated to this integral kernel is an O(2) model, which generalizes the ABJ(M) matrix model. We find its exact planar limit, and we provide detailed evid…