Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory needs an algebra of observables and an object that incorporates the information about relative phases and probabilities. The latter is the (de)coherence fun...

This paper reports "work in progress" on a project which I've titled, "The Spaces of Transnational Cultures". The aim of the project is to build on, but be methodologically different from, my earlier research on the architecture and urbanism of colonial and postcolonial cities in which the principal objective had been to demonstrate the inherently constitutive relationship between the political...

We deal with quantum spaces of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three and four dimensions. For all these cases representations of their covariant differential calculi have been worked out. The explicit formulae refer to left representations, as right representations can be easily deduced from left ones. We are going to show for...

This contribution to the proceedings of the 1999 NATO ASI on Quantum Geometry at Akureyri, Iceland, is based on notes of lectures given by A. Strominger. Topics includeN -particle conformal quantum mechanics, extended superconformal quantum mechanics and multi-black hole moduli spaces. HUTP-99/A060 hep-th/9911066 RUNHETC-99-41 2 BRITTO-PACUMIO, MICHELSON, STROMINGER AND VOLOVICH

The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal’s approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.

A noncommutative-geometric formalism of framed principal bundles is sketched, in a special case of quantum bundles (over quantum spaces) possessing classical structure groups. Quantum counterparts of torsion operators and Levi-Civita type connections are analyzed. A construction of a natural differential calculus on framed bundles is described. Illustrative examples are presented.

Gibbs field is one of the central objects of the modern probability, mathematical statistical physics and euclidean quantum field theory. Here we define and study its natural generalization for the case when the space, where the random field is defined is itself random. Moreover, this randomness is not given apriori and independently of the configuration, but rather they depend on each other, a...

We propose the following principle to study pointed Hopf algebras, or more generally, Hopf algebras whose coradical is a Hopf subalgebra. Given such a Hopf algebra A, consider its coradical filtration and the associated graded coalgebra grA. Then grA is a graded Hopf algebra, since the coradical A0 of A is a Hopf subalgebra. In addition, there is a projection π : grA → A0; let R be the algebra ...

In this article we present explicit formulae for q-integration on quantum spaces which could be of particular importance in physics, i.e. q-deformed Minkowski space and q-deformed Euclidean space in 3 or 4 dimensions. Furthermore, our formulae can be regarded as a generalization of Jackson’s q-integral to 3 and 4 dimensions and provide a new possibility for an integration over the whole space b...