相关论文: Noncommutative probability, matrix models, and qua…
A string-net model associates a vector space to a surface in terms of graphs decorated by objects and morphisms of a pivotal fusion category modulo local relations. String-net models are usually considered for spherical fusion categories,…
In this note we observe that, contrary to the usual lore, string orbifolds do not describe strings on quotient spaces, but rather seem to describe strings on objects called quotient stacks, a result that follows from simply unraveling…
A non-Hermitean random matrix model proposed a few years ago has a remarkably intricate spectrum. Various attempts have been made to understand the spectrum, but even its dimension is not known. Using the Dyson-Schmidt equation, we show…
We study the statistical mechanics of random surfaces generated by NxN one-matrix integrals over anti-commuting variables. These Grassmann-valued matrix models are shown to be equivalent to NxN unitary versions of generalized Penner matrix…
We show that the probabilistic distribution over the space in the spectator world, can be associated via noncommutative geometry (with some modifications) to a metric in which the particle lives. According to this geometrical view, the…
The recent developments in string theory suggest that the space-time coordinates should be generalized to non-commuting matrices. Postulating this suggestion as the fundamental geometrical principle, we formulate a candidate for covariant…
In this short review we outline some recent developments in understanding string orbifolds. In particular, we outline the recent observation that string orbifolds do not precisely describe string propagation on quotient spaces, but rather…
Two examples of the situation when the classical observables should be described by a noncommutative probability space are investigated. Possible experimental approach to find quantum-like correlations for classical disordered systems is…
I consider the $\mathbb{Z}_\lambda,$ $\lambda$ prime free-bosonic permutation orbifolds as interacting physical string systems at $\hat{c} = 26\lambda $. As a first step, I introduce twisted tree diagrams which confirm at the interacting…
In a recent work it has been shown that the bosonic strings could be embedded into a special class of $N=1$ fermionic strings. We argue that the superpartners of any physical state in the spectrum of this fermionic string is non-physical.…
Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
We discuss the non--perturbative formulation for $c \leq 1$ string theory. The field theory like formulation of topological and non--topological models is presented. The integral representation for arbitrary $(p,q)$ solutions is derived…
Cosmic strings in non-abelian gauge theories naturally gain a spectrum of massless, or light, excitations arising from their embedding in color and flavor space. This opens up the possibility that colliding strings miss each other in the…
We consider quotients of string and M-theory by discrete subgroups of the U-duality group. This results in what we call O-folds, which are generalisations of orbifolds and orientifolds, and generically involve non-geometric identifications…
In quantum field theory, an orbifold is a way to obtain a new theory from an old one by gauging a finite global symmetry. This definition of orbifold does not make sense for quantum gravity theories, that admit (conjecturally) no global…
Infinite-dimensional Grassmannian manifold contains moduli spaces of Riemann surfaces of all genera. This well known fact leads to a conjecture that non-perturbative string theory can be formulated in terms of Grassmannian. We present new…
Here we present an overview on the various works, in which many collaborators have contributed, regarding the interesting dipole of noncommutativity and physics. In brief, we present the features that noncommutativity triggers both in the…
Four years ago the Extended Scale Relativity (ESR) theory in C-spaces (Clifford manifolds) was proposed as the plausible physical foundations of string theory. In such theory the speed of light and the minimum Planck scale are the two…
The space-time light-cone Hamiltonian P^- of large-N matrix models for dynamical triangulations may be viewed as that of a quantum spin chain and analysed in a mean field approximation. As N -> infinity, the properties of the groundstate as…