Related papers: Root Systems and Boundary Bootstrap
A quantum $n$-particle model consisting of an open $q$-difference Toda chain with two-sided boundary interactions is placed on a finite integer lattice. The spectrum and eigenbasis are computed by establishing the equivalence with a…
We present a solution of the problem of a free massless scalar field on the half line interacting through a periodic potential on the boundary. For a critical value of the period, this system is a conformal field theory with a non-trivial…
For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with…
A simple relation between inhomogeneous transfer matrices and boundary quantum KZ equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogous to an observation by Gaudin for periodic systems. Thus…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
The integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains are considered in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of…
We study the exact solution of an $N$-state vertex model based on the representation of the $U_q[SU(2)]$ algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class…
We build up local, time translation covariant Boundary Quantum Field Theory nets of von Neumann algebras A_V on the Minkowski half-plane M_+ starting with a local conformal net A of von Neumann algebras on the real line and an element V of…
Motivated by cosmological observations, we push the cosmological bootstrap program beyond the de Sitter invariance lamppost by considering correlators that explicitly break scale invariance, thereby exhibiting primordial features. For…
We explore how matrix bootstrap techniques can be used to constrain matrix and tensor models at finite $N$, where $N$ is the dimension of the matrix/tensor, taking a Gaussian model with a quartic interaction as example. For matrix models,…
In the realm of contemporary physics, the bootstrap method is typically associated with an optimization-based approach to problem-solving. This method leverages our understanding of a specific physical problem, which is used as the…
Extending previous work on $a_2^{(1)}$, we present a set of reflection matrices, which are explicit solutions to the $a_n^{(1)}$ boundary Yang-Baxter equation. Unlike solutions found previously these are multiplet-changing $K$-matrices, and…
We study a natural family of non-local elliptic boundary problems on a compact oriented surface $\Sigma$ parametrized by the moduli space $\mathcal{M}_\Sigma$ of flat $G$-connections with framing along $\partial \Sigma$. This family…
The presence of a boundary (or defect) in a conformal field theory allows one to generalize the notion of an exactly marginal deformation. Without a boundary, one must find an operator of protected scaling dimension $\Delta$ equal to the…
We elaborate on the proposed general boundary formulation as an extension of standard quantum mechanics to arbitrary (or no) backgrounds. Temporal transition amplitudes are generalized to amplitudes for arbitrary spacetime regions. State…
A quantum field theory generalization, Baaquie, of the Heath, Jarrow, and Morton (HJM) term structure model parsimoniously describes the evolution of imperfectly correlated forward rates. Field theory also offers powerful computational…
An informal introduction to our recent work on the principal chiral model with boundary. We found that both classically integrable boundary conditions and quantum boundary S-matrices were classified by the symmetric spaces G/H. The…
Relativistic quantum field theory offers, in form of the homogeneous Bethe-Salpeter framework, a (Poincar\'e-covariant) description of bound states in terms of their underlying theory's fundamental degrees of freedom. In view of the…
Exploiting the quantum integrability condition we construct an ancestor model associated with a new underlying quadratic algebra. This ancestor model represents an exactly integrable quantum lattice inhomogeneous anisotropic model and at…
This is a review/announcement of results concerning the connection between certain exactly solvable two-dimensional models of statistical mechanics, namely loop models, and the equivariant $K$-theory of the cotangent bundle of the…