José Antonio Zapata
Centro de Ciencias
Matemáticas
UNAM Campus Morelia Morelia
CP 58190 Michoacán, México
Before being here:
Bs Physics UNAM, México
PhD Physics Penn State, USA
Postdoc RRI, India
Renormalization tailored to loop quantization
Let us consider that loop quantization as described in
the section
"Spin foam models in the continuum"
is a formalism able to define quantum field theories on a given spacetime manifold.
The definition of such theories
involves limits characterizing certain projective measures,
and these limits are the natural objects to write from the point of view of
the projective techniques inherent to loop quantization.
The missing ingredient was a constructive method for such theories;
truly nontrivial examples
seamed to be out of reach. On the other hand, the lattice gauge theory
developed by Wilson has many similarities with loop quantization, and in its
core it has a constructive procedure: Wilson's
renormalization procedure. From this point of view, loop quantized theories as
defined in the section cited above should be seen as the continuum limit of
completely renormalized lattice theories. In the article shown below this point
of view is developed and loop quantization is presented as a quantization
procedure which needed to be completed. An implementation of Wilson's
renormalization is exhibited as the missing part needed to make the quantization
procedure operational.
Loop quantization from a lattice gauge theory perspective
Jose A. Zapata,
Class.Quant.Grav. 21 (2004) L115-L122
An interacting relativistic quantum field theory
constructed by loop quantization
We had a good idea of how to implement Wilson's renormalization procedure in
the context of loop quantization;
we only needed to materialize our intuition with a
nontrivial example.
Mc Coy, Tracy and Wu proved ground-breaking results on the
convergence of the double scaling limit
of the n-point functions of the 2d Ising model. These
results let us give a concrete example of an interacting quantum field
theory defined and
constructed by loop quantization techniques.
Loop quantization as a continuum limit
Elisa Manrique, Robert Oeckl, Axel Weber, Jose A. Zapata,
Class.Quant.Grav. 23 (2006) 3393-3404