Related papers: Form factors, correlation functions and vertex ope…

We establish precise Zhu reduction formulas for Jacobi $n$-point functions which show the absence of any possible poles arising in these formulas. We then exploit this to produce results concerning the structure of strongly regular vertex…

This paper studies how many orthogonal bi-invariant complex structures exist on a metric Lie algebra over the real numbers. Recently, it was shown that irreducible Lie algebras which are additionally $2$-step nilpotent admit at most one…

Recently, \cite{Cao:2025hio} demonstrated the $2$-split for form factor under specific kinematic constraints. This factorization is analogous to that observed in scattering amplitudes. A key consequence of this structure is the presence of…

We give a brief survey of recent work on integral forms in vertex operator algebras (VOAs).

A gradient dependent formula is derived for the spinless one-particle density-matrix operator z from the differential virial theorem. A gradient dependent formula is also derived for a spinless one-particle density-matrix operator that can…

We investigate the complex reflection group $\mathfrak{G}$ associated with the octahedral group, identified as the ninth entry in the Shephard-Todd classification. We determine all irreducible representations of $\mathfrak{G}$ and compute…

We introduce new methods to describe admissible states of the six-vertex and the eight-vertex lattice models of statistical mechanics. For the six-vertex model, we view the admissible states as differential forms on a grid graph. This…

We construct integral forms containing the conformal vector $\omega$ in certain tensor powers of the Virasoro vertex operator algebra $L(\frac{1}{2},0)$, and we construct integral forms in certain modules for these algebras. When a triple…

We provide detailed arguments on how to derive properties of generalized form factors, originally proposed by one of the authors (M.K.) and Weisz twenty years ago, solely based on the assumption of "minimal analyticity" and the validity of…

We compare two different methods of computing form factors. One is the well established procedure of solving the form factor consistency equations and the other is to represent the field content as well as the particle creation operators in…

In this work we consider fermionic zero modes in the external scalar and electromagnetic field forming the vortex on a sphere. We find the correspondence between the equations for the fermions in different dimensions, find their explicit…

We prove a determinant formula for the standard integral form of a lattice vertex operator algebra.

We propose new types of integrable spinor models, generalizing the well known ones of: i) Nambu-Jona-Lasinio-Vaks-Larkin models, related to SU(N); ii) the Gross-Neveu models - SP(2N); and the iii) Zakharov-Mikhailov models - SO(N). We…

We study 3-point functions at finite temperature in the closed time path formalism. We give a general decomposition of the eight component tensor in terms of seven vertex functions. We derive a spectral representation for these seven…

Exact integral representations of spin one-point functions (ground state expectation values) are reported for the spin-1 analog of the XXZ model in the region $-1<q<0$. The method enables one to calculate arbitrary $n$-point functions in…

It is important to obtain effective operators by integrating out high energy degrees of freedom in physics. We suggest a general method of calculating accurate irrelevant operators in a scattering process without use of equation of motions.…

The leitmotif of these Notes is the idea of a vertex operator algebra (VOA) and the relationship between VOAs and elliptic functions and modular forms. This is to some extent analogous to the relationship between a finite group and its…

We consider the quantum sinh-Gordon model in this paper. Using known formulae for form factors we sum up all their contributions and obtain a closed expression for a correlation function. This expression is a determinant of an integral…

We construct embeddings of boundary algebras B into ZF algebras A. Since it is known that these algebras are the relevant ones for the study of quantum integrable systems (with boundaries for B and without for A), this connection allows to…

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…