INVITATION for
PUBLIC LECTURE by
David
Brydges, University of British Columbia,
Canada
May 20, 2008
EURANDOM, Laplace Building TU/e, Green Lecture Room (LG 1.105)
PROGRAMME
* For organizational reasons please send an email to coolen@eurandom.tue.nl if you plan to attend.
15.15  Coffee/Tea 
15.25  Welcome
by
the Dean of the Department of
Mathematics and Computer Science. Eindhoven University of Technology Introduction by Professor F. den Hollander, Leiden University 
15.30

Would you rather be a field or a particle? This will be an attempt to describe in an elementary way some of the structural aspects of quantum field theory (QFT), which I have always found to be very appealing, and yet not commonly known outside theoretical physics.
In particular, 
16.30 h.  Reception 
INVITATION for LECTURE SERIES by
David
Brydges, University of British Columbia,
Canada
Friday June 13; 35.15 pm. (LG 1.105)
Fridays June 20, June 27, July 4 & July 11; 1012.15 am (LG 1.105,
on July 4  LG 1.110)
* Please send an email to coolen@eurandom.tue.nl if you plan to attend.
The lectures will cover
1. Models and their representation in terms of Gaussian integrals
2. Hierarchical models and the action of the renormalisation group
3. Renormalisation group for models on the Euclidean lattice
Abstract
In the theory of critical phenomena in statistical mechanics, the idea of
a scaling limit is exemplified by observing a very long selfavoiding walk
from far away so that individual steps become invisible and one sees (the
ocupation density of) a path in the continuum. The scaling limit is the
probability law for this random continuum path. The Renormalisation Group (RG)
is a nascent program to construct and classify scaling limits. It is based
on the Nobel prize work of Ken Wilson. RG is a map acting on a space of
statistical mechanical models. Models are probability measures on random
fields and RG acts on a model by integrating out the short distance
fluctuations giving rise to a new model whose typical random field has the
same long distance fluctuations but suppressed short distance fluctuations.
Finding scaling limits corresponds to proving that the action of RG is
almost equivalent to scaling. In order to apply our form of RG one must
first express the problem as a “multiplicative perturbation” of the
“massless Gaussian measure”. I will define these terms and show that a range
of models can be put in this form, including finding the endtoend distance
of selfavoiding walk. Another simpler model presenting the same basic
difficulties is “dipoles on the Euclidean lattice”. This is closely related
to determining correlations for the “anharmonic bedspring” which is a model
for sound waves in a crystal. I will use hierarchical models and then this
dipole model as my main examples for detailed analysis.
My Park City Lecture notes posted
here give an idea of
what to expect.
Last modified:
030909
Maintained by L. Coolen