Related papers: Form Factors of 2-D Integrable Models Using Radial…
We extend previous calculations of the non-local form factors of semiclassical gravity in $4D$ to include the Einstein-Hilbert term. The quantized fields are massive scalar, fermion and vector fields. The non-local form factor in this case…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
Starting from the finite volume form factors of local operators, we show how and under which hypothesis the $c=1$ free boson conformal field theory in two-dimensions emerges as an effective theory governing the large-distance regime of…
The form-factor bootstrap approach is applied to the perturbed minimal models $M_{2,2n+3}$ in the direction of the primary field $\phi_{1,3}$. These theories are integrable and contain $n$ massive scalar particles, whose $S$--matrix is…
Quantum--mechanical operators corresponding to canonical momentum and position of a point--like particle, which follow from the quantum field theory in the general Riemannian space-time, satisfy generally to a deformation of the canonical…
Based on any chiral vertex operator algebra satisfying a suitable finiteness condition, the semisimplicity of the zero-mode algebra as well as a regularity for induced modules, we construct conformal field theory over the projective line…
The symmetry group of the staggered Fermion transfer matrix in a spatial direction is constructed at finite temperature. Hadron-like operators carrying irreducible representations of this group are written down from the breaking of the zero…
The hamiltonian formalism is developed for the sine-Gordon model on the space-time light-like lattice, first introduced by Hirota. The evolution operator is explicitely constructed in the quantum variant of the model, the integrability of…
The ${\mathcal D}$-pseudo-boson formalism is illustrated with two examples. The first one involves deformed complex Hermite polynomials built using finite-dimensional irreducible representations of the group ${\rm GL}(2,{\mathbb C})$ of…
We investigate the nucleon and pion gravitational $D$-form factors, by fitting a $\sigma/f_0(500)$-meson pole, together with a background term, to lattice data at $m_\pi \approx 170\text{MeV}$. We find that the fitted residues are…
We study on-shell and off-shell properties of the supersymmetric sinh-Gordon and perturbed SUSY Yang-Lee models using the thermodynamic Bethe ansatz and form factors. Identifying the supersymmetric models with the Eight Vertex Free Fermion…
Surprising links between the deformation of 2D quantum field theories induced by the composite $\textrm{T} \bar{\textrm{T}}$ operator, effective string models and the $AdS/$CFT correspondence, have recently emerged. The purpose of this…
A bosonization scheme of the $q$-vertex operators of $\uqa$ for arbitrary level is obtained. They act as intertwiners among the highest weight modules constructed in a bosonic Fock space. An integral formula is proposed for $N$-point…
We present a free field realisation for the vertex operator algebra associated to the genus-two, class $\mathcal{S}$ superconformal field theory of type $\mathfrak{a}_1$. The free field realisation is in the style of recent work by the…
Formation control of autonomous agents can be seen as a physical system of individuals interacting with local potentials, and whose evolution can be described by a Lagrangian function. In this paper, we construct and implement forced…
Applications of the integrable system techniques to the non-equilibrium transport problems are discussed. We describe one-dimensional electrons tunneling through a point-like defect either by the s-d exchange (Kondo) mechanism, or via the…
Some aspects of two-dimensional gravity coupled to matter fields, especially to the Sine-Gordon-model are examined. General properties and boundary conditions of possible soliton-solutions are considered. Analytic soliton-solutions are…
A perturbation theory for Massive Thirring Model (MTM) in radial quantization approach is developed. Investigation of the twisted sector in this theory allows us to calculate the vacuum expectation values of exponential fields $ exp iaphi…
This paper is the first in a series on graphical calculus for quantum vertex operators. We establish in great detail the foundations of graphical calculus for ribbon categories and braided monoidal categories with twist. We illustrate the…
Causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory. By specializing, we recover earlier notions like fermion systems in discrete space-time, the fermionic projector and…