Related papers: Generalized Quantum Inverse Scattering
Recently there has been much effort in developing a quantum generalisation of reference frame transformations. Despite important progress, a complete understanding of their principles is still lacking. In particular, we argue that previous…
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are…
It is shown that the operator algebraic setting of local quantum physics leads to a uniqueness proof for the inverse scattering problem. The important mathematical tool is the thermal KMS aspect of wedge-localized operator algebras and its…
A generalization of the generalized inverse Weibull distribution so-called transmuted generalized inverse Weibull dis- tribution is proposed and studied. We will use the quadratic rank transmutation map (QRTM) in order to generate a…
A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a Central Limit Theorem generalized in the presence of specific correlations between the relevant random variables.…
By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the…
A deformation of the canonical algebra for kinematical observables of the quantum field theory in Minkowski space-time has been considered under the condition of Lorentz invariance. A relativistic invariant algebra obtained depends on…
We construct a quantum integrable model which is an $R$-matrix generalization of the Calogero-Moser system, based on the Baxter-Belavin elliptic $R$-matrix. This is achieved by introducing $R$-matrix Dunkl operators so that commuting…
In this work we demonstrate a simple way to implement the quantum inverse scattering method to find eigenstates of spin-1/2 XXX Gaudin magnets in an arbitrarily oriented magnetic field. The procedure differs vastly from the most natural…
The universal covering of SO(3) is modelled as a reflection group G_R in a representation independent fashion. For relativistic quantum fields, the Unruh effect of vacuum states is known to imply an intrinsic form of reflection symmetry,…
Quantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has matured over the past fifteen years to a mathematically rigorous candidate quantum field theory of the gravitational field. The features that distinguish it from…
The inverse quantum scattering problem for the perturbed Bessel equation is considered. A direct and practical method for solving the problem is proposed. It allows one to reduce the inverse problem to a system of linear algebraic…
The inverse scattering theory is a basic tool to solve linear differential equations and some Partial Differential Equations (PDEs). Using this theory the Korteweg-de Vries (KdV), the family of evolutionary Non Linear Schrodinger (NLS)…
STU supergravity becomes an integrable system for solutions that effectively only depend on two variables. This class of solutions includes the Kerr solution and its charged generalizations that have been studied in the literature. We here…
With appropriate modifications, the multi-spin Klein-Gordon (KG) equation of quantum field theory can be adapted to curved spacetime for spins 0,1,1/2. The associated particles in the microworld then move as a wave at all spacetime…
We establish a direct link between Dunkl operators and quantum Lax matrices $\mathcal L$ for the Calogero--Moser systems associated to an arbitrary Weyl group $W$ (or an arbitrary finite reflection group in the rational case). This…
A new method is introduced to derive general recurrence relations for off-shell Bethe vectors in quantum integrable models with either type $\mathfrak{gl}_n$ or type $\mathfrak{o}_{2n+1}$ symmetries. These recurrence relations describe how…
In this paper we consider an inverse problem for the $n$-dimensional random Schr\"{o}dinger equation $(\Delta-q+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a Gaussian random…
This paper considers a generalisation of the idea of a Hopf algebra in which a commutative ring replaces the field in the unit and counit. It is motivated by an example from the inverse scattering formalism for solitons. We begin with the…
A simple backreaction problem in quantum mechanics, the full quantum anharmonic oscillator, and quantum parametric resonance are studied using Renormalization Group techniques for global asymptotic analysis. In this short note this…