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We have constructed and solved various one-dimensional quantum mechanical models which have quantum algebra symmetry. Here we summarize this work, and also present new results on graded models, and on the so-called string solutions of the…

We discuss how to recognize the constellations seen in the Majorana representation of quantum states. Then we give explicit formulas for the metric and symplectic form on SU(2) orbits containing general number states. Their metric and…

We find electric string solutions in Yang-Mills-Higgs theory.

We compute the high energy entropy and the equation of state of a gas of open superstrings in the infinite volume limit focusing on the calculation of the number of strings as a function of energy and volume. We do it in the fixed…

We review the status of low-scale string theories and large extra-dimensions. After an overview on different string realizations, we discuss some of the main important problems and we summarize present bounds on the size of possible…

As is known, tetrahedron equations lead to the commuting family of transfer-matrices and provide the integrability of corresponding three-dimensional lattice models. We present the modified version of these equations which give the…

This essay presents a critical evaluation of the concepts of string theory and its impact on particle physics. The point of departure is a historical review of four decades of ST within the broader context of six decades of failed attempts…

This paper introduces the notion of tubular eigenvalues of third-order tensors with respect to T-products of tensors and analyzes their properties. A focus of the paper is to discuss relations between tubular eigenvalues and two alternative…

We discuss charged string solutions of the effective equations of D=4 heterotic string theory with non-constant dilaton and modulus fields. The effective action contains a generic moduli-dependent coupling function in the gauge field…

Using a modified version of the tetrahedron equations we construct a new family of $N$-state three-dimensional integrable models with commuting two-layer transfer-matrices. We investigate a particular class of solutions to these equations…

We develop the intersection theory associated to immersed, oriented and mea- sured solenoids, which were introduced in arXiv:0910.2836.

We propose a simple and accurate model for the electron static structure factors (and corresponding pair-correlation functions) of the 3D unpolarized homogeneous electron gas. Our spin-resolved pair-correlation function is built up with a…

The angular part of the Faddeev equations is solved analytically for s-states for two-body square-well potentials. The results are, still analytically, generalized to arbitrary short-range potentials for both small and large distances. We…

We briefly review superstring theories, highlighting the important concepts, developments, and open problems of the subject.

An exact, number-conserving solution to the generalized, orbit-dependent pairing problem is derived by introducing an infinite-dimensional algebra. A method for obtaining eigenvalues and eigenvectors of the corresponding Hamiltonian is also…

The Riemann-Hilbert problems for multiple orthogonal polynomials of types I and II are used to derive string equations associated to pairs of Lax-Orlov operators. A method for determining the quasiclassical limit of string equations in the…

We present n-1 different embeddings of string polytopes of type A. We characterize their compatibility with the crystal structure on the string polytopes, and formulate a conjecture describing how to obtain n-1 different atomic…

We present and discuss explicit solutions to the non-abelian self-dual string equation as well as to the non-abelian self-duality equation in six dimensions. These solutions are generalizations of the 't Hooft-Polyakov monopole and the BPST…

We quantify various possible entanglement measures for the four particles GHZ entangled state that has been produced experimentally [C. Sackett et al, Nature 404, 256-259 (2000)].

We study the polygamy property for tripartite and multipartite quantum systems. In tripartite system, we build a solution set for polygamy in tripartite system and find a lower bound of the set, which can be a sufficient and necessary…