相关论文: A Dynamical 2-dimensional Fuzzy Space
Several versions of fuzzy four-dimensional de Sitter space are constructed using the noncommutative frame formalism. Although all noncommutative spacetimes which are found have commutative de Sitter metric as a classical limit, the algebras…
The product of a non-commutative matrix spectral triple with a simple two-dimensional internal space is considered. This is interpreted as a non-commutative spacetime that contains one charged Dirac fermion and its antiparticle. The inner…
It is argued that a noncommutative geometry of spacetime leads to a reconciliation of electromagnetism and gravitation while providing an underpinning to Weyl's geometry. It also leads to a cosmology consistent with observation. A few other…
A review is made of recent efforts to add a gravitational field to noncommutative models of space-time. Special emphasis is placed on the case which could be considered as the noncommutative analog of a parallelizable space-time. It is…
A non-commutative structure for de Sitter spacetime is naturally introduced by replacing ("fuzzyfication") the classical variables of the bulk in terms of the dS analogs of the Pauli-Lubanski operators. The dimensionality of the fuzzy…
We analyze several families of two-dimensional quantum random walks. The feasible region (the region where probabilities do not decay exponentially with time) grows linearly with time, as is the case with one-dimensional QRW. The limiting…
In this paper the connection between quantum field theories on flat noncommutative space(-times) in Euclidean and Lorentzian signature is studied for the case that time is still commutative. By making use of the algebraic framework of…
We find an infinite number of noncommutative geometries which posses a differential structure. They generalize the two dimensional noncommutative plane, and have infinite dimensional representations. Upon applying generalized coherent…
We use the non-Abelian DBI action to study the dynamics of $N$ coincident $Dp$-branes in an arbitrary curved background, with the presence of a homogenous world-volume electric field. The solutions are natural extensions of those without…
Four-dimensional manifolds with changing signature are obtained by taking the large $N$ limit of fuzzy $CP^2$ solutions to a Lorentzian matrix model. The regions of Lorentzian signature give toy models of closed universes which exhibit…
We propose a toy model of quantum gravity in two dimensions with Euclidean signature. The model is given by a kind of discretization which is different from the dynamical triangulation. We show that there exists a continuum limit and we can…
We study a formal extension of the Dirac equation in the framework of a non-commutative two-sheeted space-time. It is shown that this approach naturally extends the classical Dirac theory by doubling the number of fermionic states, which…
A Wick rotation in the lapse (not in time) is introduced that interpolates between Riemannian and Lorentzian metrics on real manifolds admitting a codimension-one foliation. The definition refers to a fiducial foliation but covariance under…
A ``Wick rotation'' is applied to the noncommutative sphere to produce a noncommutative version of the hyperboloids. A harmonic basis of the associated algebra is given. It is noted that, for the one sheeted hyperboloid, the vector space…
We conjecture an embedding operator which assigns, to any 2n+1 hermitian matrices, a 2n-dimensional hypersurface in flat (2n + 1)-dimensional Euclidean space. This corresponds to precisely defining a fuzzy D(2n)-brane corresponding to N…
A review is made of recent efforts to define linear connections and their corresponding curvature within the context of noncommutative geometry. As an application it is suggested that it is possible to identify the gravitational field as a…
In this paper, we discuss two features of the noncommmutative geometry and spectral action approach to the Standard Model: the fact that the model is inherently Euclidean, and that it requires a quadrupling of the fermionic degrees of…
In two space dimensions and one time dimension a wave changes its shape even in the absence of a dispersive medium. However, this anomalous dispersive behavior in empty two-dimensional space does not occur if the wave dynamics is described…
We perform quantization of a model in which gravity is coupled to a circular dust shell in 2+1 spacetime dimensions. Canonical analysis shows that momentum space of this model is ADS^2-space, and the global chart for it is provided by the…
In this paper we extend the standard differential geometric theory of Hamiltonian dynamics to noncommutative spaces, beginning with symplectic forms. Derivations on the algebra are used instead of vector fields, and interior products and…