ar X iv : p hy si cs / 9 71 20 19 v 1 [ m at h - ph ] 1 1 D ec 1 99 7 Symmetries of particle motion

ar X iv : d g - ga / 9 71 20 20 v 1 3 0 D ec 1 99 7 Weinstein Conjecture and GW Invariants

ar X iv : m at h - ph / 9 90 90 25 v 1 2 1 Se p 19 99 The symmetries of the Manton superconductivity model

The symmetries and conserved quantities of Manton's modified superconductiv-ity model with non-relativistic Maxwell-Chern-Simons dynamics (also related to the Quan-tized Hall Effect) are obtained in the " Kaluza-Klein type " framework of Duval et al. 1. Introduction Recently [1], Manton proposed a modified version of the Landau-Ginzburg theory of superconductivity. His equations, defined on (2 ...

ar X iv : m at h - ph / 9 81 20 09 v 1 1 3 D ec 1 99 8 Quantum dots A survey of rigorous results

ar X iv : m at h - ph / 9 91 20 06 v 1 7 D ec 1 99 9 Compact Quantum Groupoids

Quantum groupoids are a joint generalization of groupoids and quantum groups. We propose a definition of a compact quantum groupoid that is based on the theory of C *-algebras and Hilbert bimodules. The essential point is that whenever one has a tensor product over C in the theory of quantum groups, one now uses a certain tensor product over the base algebra of the quantum groupoid.

ar X iv : g r - qc / 9 71 20 19 v 1 3 D ec 1 99 7 Lecture Notes on General Relativity

These notes represent approximately one semester’s worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein’s equations, and three applications: gravitational radiation, black holes, and cosmology. Individual chapters, and potentially updated versions, can be found at http://itp.ucsb.edu/~carroll/not...