相关论文: Unitarity of the SoV Transform for $\mathrm{SL}(2,…

The integrable system is introduced based on the Poisson $ rs $-matrix structure. This is a generalization of the Gaudin magnet, and in SL(2) case isomorphic to the generalized Neumann model. The separation of variables is discussed for…

We propose a way to separate variables in a rational integrable $\mathfrak{gl}(n)$ spin chain with an arbitrary finite-dimensional irreducible representation at each site and with generic twisted periodic boundary conditions. Firstly, we…

We construct the integrable model corresponding to the $\N=2$ supersymmetric SU(N) gauge theory with matter in the antisymmetric representation, using the spectral curve found by Landsteiner and Lopez through M Theory. The model turns out…

We examine which of the compact connected Lie groups that act transitively on spheres of different dimensions leave the unique spin structure of the sphere invariant. We study the notion of invariance of a spin structure and prove this…

We study the general L_0-regular gl(2) spin chain, i.e. a chain where the sites {i,i+L_0,i+2L_0,...} carry the same arbitrary representation (spin) of gl(2). The basic example of such chain is obtained for L_0=2, where we recover the…

We propose a general scheme for separation of variables in the integrable Hamiltonian systems on orbits of the loop algebra $\mathfrak{sl}(2,\Complex)\times \mathcal{P}(\lambda,\lambda^{-1})$. In particular, we illustrate the scheme by…

We derive the spin-statistics theorem in both relativistic and non-relativistic first-quantized form, extending considerably the earlier proofs. Our derivation is based on the representation theories of the groups SU (2) and SL(2,C), latter…

Just like the vector bosons in Abelian and non-Abelian gauge theories, gravitons can attain mass by spontaneous local symmetry breaking. The question is whether this can happen in a Lorentz-invariant way. We consider the use of four scalar…

We propose a non-standard separation of variables for the classical integrable XXX and XXZ spin chains with degenerate twist matrix. We show that for the case of such twist matrices one can interchange the role of classical separating…

Recent work has characterised rigorously what it means for one quantum system to simulate another, and demonstrated the existence of universal Hamiltonians -- simple spin lattice Hamiltonians that can replicate the entire physics of any…

We consider the Hamiltonian of the closed $SU(2)_{q}$ invariant chain. We project a particular class of statistical models belonging to the unitary minimal series. A particular model corresponds to a particular value of the coupling…

We analyze the tree-level 2->2 scattering of massive spin-2 bosons in a theory with only relevant and marginal operators and extract the sum rules on the coupling constants and masses required to achieve tree-level unitarity to very high…

In this paper we consider the spin 1/2 highest weight representations for the 6-vertex Yang-Baxter algebra on a finite lattice and analyze the integrable quantum models associated to the antiperiodic transfer matrix. For these models, which…

In this paper we take further steps towards developing the separation of variables program for integrable spin chains with gl(N) symmetry. By finding, for the first time, the matrix elements of the SoV measure explicitly we were able to…

The control of spins and spin to charge conversion in organics requires understanding the molecular spin-orbit coupling (SOC), and a means to tune its strength. However, quantifying SOC strengths indirectly through spin relaxation effects…

We develop a general formalism of duality rotations for bosonic conformal spin-$s$ gauge fields, with $s\geq 2$, in a conformally flat four-dimensional spacetime. In the $s=1$ case this formalism is equivalent to the theory of…

We investigate the relation between the local variables of a discrete integrable lattice system and the corresponding separation variables, derived from the associated spectral curve. In particular, we have shown how the inverse…

We present a multiparameter generalization of the St\"ackel transform (the latter is also known as the coupling-constant metamorphosis) and show that under certain conditions this generalized St\"ackel transform preserves the Liouville…

In this work we study symmetry fractionalization of vison excitations in topological $\mathbb{Z}_2$ spin liquids. We show that in the presence of the full $\mathrm{SO}(3)$ spin rotational symmetry and if there is an odd number of…

A spontaneously broken SU(2) theory is the simplest generalization of the Abelian Higgs model, containing three equally massive vector bosons and a single Higgs scalar. A strictly diagrammatic proof is presented of the tree-level unitarity…