相关论文: Quantum Matrix Pairs
We produce neccessary and sufficient conditions for pairs of quantum minors in the quantized coordinate algebra $\Bbb{C}_q[Mat_{k \times m}]$ to quasi-commute. In addition we study the combinatorics of maximal (by inclusion) families of…
In ordinary, non-relativistic, quantum physics, time enters only as a parameter and not as an observable: a state of a physical system is specified at a given time and then evolved according to the prescribed dynamics. While the state can,…
Reciprocal pairs of quantum channels are defined as completely positive transformations which admit a rigid, distance-preserving, yet not completely-positive transformation that allows to reproduce the outcome of one from the corresponding…
In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…
Usually the generators of a quantum group are assumed to be commutative with the noncommuting coordinates of a quantum plane. We have relaxed the assumption and investigated its consequences. Not only does a two-parameter quantum group…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We…
We clarify the correspondence between the two approaches to quantum graphs: via quantum adjacency matrices and via quantum relations. We show how the choice of a (possibly non-tracial) weight manifests itself on the quantum relation side…
In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…
A quantum deformation of the adjoint action of the special linear group on the variety of nilpotent matrices is introduced. New non-embedded quantum homogeneous spaces are obtained related to certain maximal coadjoint orbits, and known…
In this paper a new concept related to the frame theory is introduced; the notion of pair frame. By investigating some properties of such frames, it is shown that pair frames are a generalization of ordinary frames. Some classes of of them…
We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is…
We formulate a notion of the quantum automorphism group of a $2$-graph. After some preliminary computations, we define quantum isomorphism between a pair of $2$-graphs. We produce a `non-trivial' example of a pair of $2$-graphs that are not…
Classical symmetric pairs consist of a symmetrizable Kac-Moody algebra $\mathfrak{g}$, together with its subalgebra of fixed points under an involutive automorphism of the second kind. Quantum group analogs of this construction, known as…
A general definition has been proposed recently of a linear connection and a metric in noncommutative geometry. It is shown that to within normalization there is a unique linear connection on the quantum plane and there is no metric.
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
A quantum symmetric pair is a quantization of the symmetric pair of universal enveloping algebras. Recent development suggests that most of the theory for quantum groups can be generalised to the setting of quantum symmetric pairs. In this…
It is argued that quantum gravity has an interpretation as a topological field theory provided a certain constraint from the path intergral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for…