相关论文: A Lie Algebra for Closed Strings, Spin Chains and …

In this paper, we construct nonlinear coherent states for the generalized isotonic oscillator and study their non-classical properties in-detail. By transforming the deformed ladder operators suitably, which generate the quadratic algebra,…

We introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise non-linear operations. We then formulate an…

We discuss heterotic string theories in two dimensions with gauge groups Spin(24) and Spin(8) x E_8. After compactification the theories exhibit a rich spectrum of states with both winding and momentum. At special points some of these…

We present an algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter. We start by showing how to connect different…

Bilinear systems emerge in a wide variety of fields as natural models for dynamical systems ranging from robotics to quantum dots. Analyzing controllability of such systems is of fundamental and practical importance, for example, for the…

A hidden gauge theory structure of quantum mechanics which is invisible in its conventional formulation is uncovered. Quantum mechanics is shown to be equivalent to a certain Yang-Mills theory with an infinite-dimensional gauge group and a…

Quantum simulations of non-Abelian gauge theories require efficient mappings onto quantum computers and practical state preparation and measurement procedures. A truncation of the Hilbert space of non-Abelian lattice gauge theories with…

The Lie algebroids are generalization of the Lie algebras. They arise, in particular, as a mathematical tool in investigations of dynamical systems with the first class constraints. Here we consider canonical symmetries of Hamiltonian…

We examine several aspects of the formulation of M(atrix)-Theory on ALE spaces. We argue for the existence of massless vector multiplets in the resolved $A_{n-1}$ spaces, as required by enhanced gauge symmetry in M-Theory, and that these…

We study order parameters in one-dimensional quantum lattice models with finite invertible or non-invertible symmetry. We investigate what properties a string operator must satisfy in order to acquire a non-vanishing expectation value in a…

Starting from deformed quantum Heisenberg Lie algebras some realizations are given in terms of the usual creation and annihilation operators of the standard harmonic oscillator. Then the associated algebra eigenstates are computed and give…

Hom-Lie algebras are non-associative algebras generalizing Lie algebras by twisting the Jacobi identity by an endomorphism. The main examples are algebras of twisted derivations (i.e., linear maps with a generalized Leibniz rule). Such…

M(atrix) theory on an orbifold and classical two-branes therein are studied with particular emphasis to heterotic M(atrix) theory on $S_1/Z_2$ relevant to strongly coupled heterotic and dual Type IA string theories. By analyzing orbifold…

The Lie product and the order relation are viewed as defining structures for Hamiltonian dynamical systems. Their admissible combinations are singled out by the requirement that the group of the Lie automorphisms be contained in the group…

Open and Closed super-string field theories are constructed in an event-symmetric target space. The partition functions of Statistical and Quantum models are constructed in terms of invariants defined on Lie-algebra representations. An…

This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…

We consider a class of conformal models describing closed strings in axially symmetric stationary magnetic flux tube backgrounds. These models are closed string analogs of the Landau model of a particle in a magnetic field or the model of…

Lately, to provide a solid ground for quantization of the open string theory with a constant B-field, it has been proposed to treat the boundary conditions as hamiltonian constraints. It seems that this proposal is quite general and should…

We develop a theory of edge states based on the Hermiticity of Hamiltonian operators for tight-binding models defined on lattices with boundaries. We describe Hamiltonians using shift operators which serve as differential operators in…

Tensor-network methods enable probing dynamics of strongly interacting quantum many-body systems, including gauge theories, via Hamiltonian simulation, hence bypassing sign problems. They also have the potential to inform efficient…