Related papers: The Many Faces of the Chiral Potts Model
We demonstrate that the $\tau^{(j)}$-matrices in the superintegrable chiral Potts model possess the Onsager algebra symmetry for their degenerate eigenvalues. The Fabricius-McCoy comparison of functional relations of the eight-vertex model…
Quark models have a more than 60-year history and through this time they served as a powerful investigation and prediction tool in hadronic physics. In recent years, a lot of new experimental information has been arriving on hadrons that do…
We give a characterization of connected solvable groups in terms of the existence of representations with certain geometric properties. The existence of such representations for the group of upper triangular matrices played an important…
The implications of chiral symmetry for the quark model are discussed. In particular its connection with the meson-baryon approach is outlined. It is stressed that in the closure approximation, where the intermediate baryon states are used…
We study the quasi-particle spectrum of the integrable three-state chiral Potts chain in the massive phase by combining a numerical study of the zeroes of associated transfer matrix eigenvalues with the exact results of the ferromagnetic…
The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper…
Chiral perturbation theory is the effective field theory of the Standard Model at low energies. After a short introduction and overview, I discuss three topics where the chiral approach leads to a deeper understanding of low-energy hadron…
A spin-1/2 chain model that includes three spin interactions can effectively describe the dynamics of two species of bosons trapped in an optical lattice with a triangular-ladder configuration. A perturbative theoretical approach and…
By controlling the vortex core energy, the three-state ferromagnetic Potts model can exhibit two types of topological paradigms, including the quasi-long-range ordered phase and the vortex lattice phase [PRL 116, 097206 (2016)]. Here, by…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
The quantum numbers of the chiral soliton are derived for an arbitrary number of colors and flavors.
We consider Diagram algebras, $\Dg(G)$ (generalized Temperley-Lieb algebras) defined for a large class of graphs $G$, including those of relevance for cubic lattice Potts models, and study their structure for generic $Q$. We find that these…
The main result of this article is an application of the theory of invariant convex cones of Lie algebras to the study of unitary representations of Lie supergroups. It also includes an exposition of recent results of the second author on…
For many finite groups, the Inverse Galois Problem can be approached through modular/automorphic Galois representations. This is a report explaining the basic strategy, ideas and methods behind some recent results. It focusses mostly on the…
We consider the perturbations of the 3-state Potts conformal field theory introduced by Cardy as a description of the chiral 3-state Potts model. By generalising Zamolodchikov's counting argument and by explicit calculation we find new…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
Hadronic interactions are discussed within the context of the constituent quark model. The "Quark Born Diagram" methodology is outlined, extensive applications to meson-meson and meson-baryon interactions are discussed, and general features…
We survey recent developments on rationality problems for algebraic varieties, with a particular emphasis on cycle-theoretic and combinatorial methods and their applications to hypersurfaces.
Cycloids are particular Petri nets for modelling processes of actions or events. They belong to the fundaments of Petri's general systems theory and have very different interpretations, ranging from Einstein's relativity theory and…
We summarize recent progress in the understanding of fixed point resolution for conformal field theories. Fixed points in both coset conformal field theories and non-diagonal modular invariants which describe simple current extensions of…