We introduce a simple coordinate system covering half of de Sitter space. The new coordinates have several attractive properties: the time direction is a Killing vector, the metric is smooth at the horizon, and constant-time slices are just flat Euclidean space. We demonstrate the usefulness of the coordinates by calculating the rate at which particles tunnel across the horizon. When self-gravi...

We study the large N reduced model of D-dimensional Yang-Mills theory with special attention to the dynamical aspects related to the eigenvalues of the N ×N matrices, which correspond to the space-time coordinates in the IIB matrix model. We define a quantity which represents the uncertainty of the space-time coordinates and show that it is of the same order as the extent of the space time, whi...

We study the large N reduced model of D-dimensional Yang-Mills theory with special attention to the dynamical aspects related to the eigenvalues of the N ×N matrices, which correspond to the space-time coordinates in the IIB matrix model. We define a quantity which represents the uncertainty of the space-time coordinates and show that it is of the same order as the extent of the space time, whi...

Quantum theory of field (extended) objects without a priori space-time geometry has been represented. Intrinsic coordinates in the tangent fibre bundle over complex projective Hilbert state space CP (N − 1) are used instead of space-time coordinates. The fate of quantum system modeled by the generalized coherent states is rooted in this manifold. Dynamical (state-dependent) space-time arises on...

An attempt to build quantum theory of field (extended) objects without a priori space-time geometry has been represented. Space-time coordinates are replaced by the intrinsic coordinates in the tangent fibre bundle over complex projective Hilbert state space CP (N − 1). The fate of quantum system mod-eled by the generalized coherent states is rooted in this manifold. Dynamical (state-dependent)...

Isomorphisms of separable Hilbert spaces are analogous to isomorphisms of n-dimensional vector spaces. However, while n-dimensional spaces in applications are always realized as the Euclidean space Rn, Hilbert spaces admit various useful realizations as spaces of functions. In the paper this simple observation is used to construct a fruitful formalism of local coordinates on Hilbert manifolds. ...

It is possible to construct representations of the Lorentz group using four-dimensional harmonic oscillators. This allows us to construct threedimensional wave functions with the usual rotational symmetry for space-like coordinates and one-dimensional wave function for time-like coordinate. It is then possible to construct a representation of the Poincaré group for a massive particles having th...