23,798 research outputs found
Geometric flows and (some of) their physical applications
The geometric evolution equations provide new ways to address a variety of
non-linear problems in Riemannian geometry, and, at the same time, they enjoy
numerous physical applications, most notably within the renormalization group
analysis of non-linear sigma models and in general relativity. They are divided
into classes of intrinsic and extrinsic curvature flows. Here, we review the
main aspects of intrinsic geometric flows driven by the Ricci curvature, in
various forms, and explain the intimate relation between Ricci and Calabi flows
on Kahler manifolds using the notion of super-evolution. The integration of
these flows on two-dimensional surfaces relies on the introduction of a novel
class of infinite dimensional algebras with infinite growth. It is also
explained in this context how Kac's K_2 simple Lie algebra can be used to
construct metrics on S^2 with prescribed scalar curvature equal to the sum of
any holomorphic function and its complex conjugate; applications of this
special problem to general relativity and to a model of interfaces in
statistical mechanics are also briefly discussed.Comment: 18 pages, contribution to AvH conference Advances in Physics and
Astrophysics of the 21st Century, 6-11 September 2005, Varna, Bulgari
Abstract State Machines 1988-1998: Commented ASM Bibliography
An annotated bibliography of papers which deal with or use Abstract State
Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm
Combinatorial quantization of the Hamiltonian Chern-Simons theory I
Motivated by a recent paper of Fock and Rosly \cite{FoRo} we describe a
mathematically precise quantization of the Hamiltonian Chern-Simons theory. We
introduce the Chern-Simons theory on the lattice which is expected to reproduce
the results of the continuous theory exactly. The lattice model enjoys the
symmetry with respect to a quantum gauge group. Using this fact we construct
the algebra of observables of the Hamiltonian Chern-Simons theory equipped with
a *-operation and a positive inner product.Comment: 49 pages. Some minor corrections, discussion of positivity improved,
a number of remarks and a reference added
Chiral Observables and Modular Invariants
Various definitions of chiral observables in a given Moebius covariant
two-dimensional theory are shown to be equivalent. Their representation theory
in the vacuum Hilbert space of the 2D theory is studied. It shares the general
characteristics of modular invariant partition functions, although SL(2,Z)
transformation properties are not assumed. First steps towards classification
are made.Comment: 28 pages, 1 figur
- …