Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

Wojciech de Roeck
Universität Heidelberg
Diffusion in Hamiltonian models
DMV Tagung 2011 - Köln, 19. - 22. September
Irreversible phenomena like diffusion and thermalization obviously occur in our world, which is described
by deterministic and time-reversible equations (Newton’s equations of motion or the Schrödinger equation
in quantum mechanics). However, up to today we seem to lack the tools to describe and derive these
phenomena rigorously (apart from a few special models). In physics, one usually models them by
stochastic evolution equations and the transition from deterministic equations to stochastic ones remains
a leap of faith. Our work treats one of the simplest possible models: a quantum particle interacting with a
gas of bosons. With the help of a time-dependent renormalization group analysis, we prove diffusion.
Klaus Fredenhagen
Universität Hamburg
Epstein-Glaser renormalization and Batalin-Vilkovisky formalism
The Batalin-Vilkovisky formalism for field theories with gauge symmetries is revisited. It is shown that the
step from the classical theory to the quantum theory, which is usually discussed via the path integral,
can be performed by the renormalized time ordering operator which is obtained by a generalization of
Epstein-Glaser renormalization.
Hanno Gottschalk
Bergische Universität Wuppertal
On the Anti-de-Sitter / conformal field theory conjecture from a Euclidean quantum field
standpoint
The symmetry group on the Anti-de-Sitter space acts as conformal group on its boundary. It is shown that
quantum fields on Euclidean AdS - when resticted via suitable scaling - indeed fulfill conformal invariance
on the boundary. Even in the case of non-interacting fields some new renormalization factors are required.
In the case of interacting fields in AdS2 or fields with cut offs in arbitrary dimensions a new kind an
somewhat intriguing infra-red problems arises.
While the approach taken here does not reflect the richness of Maldacena’s AdS/CFT conjecture on
Supergravity and Yang-Mills theory, the AdS/CFT problem for Euclidean quantum fields allows statement
and proof of some rigorous results on the basis of what has been established in Constructive QFT.
Literatur
M. Dütsch, K.-H. Rehren, A comment on the dual field in the AdS-CFT correspondence, Lett. Math. Phys.
62 (2002) 171-184.
Gottschalk, H, Thaler, H. (2008),AdS/CFT correspondence in the Euclidean context, Commun. Math.
Phys., 277, 83 - 100.
E.Witten, Anti-de Sitter space and holography, Adv. Theor.Math. Phys. 2 (1998) 253-291.
74