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


Spin foam models in the continuum /
compatibility with canonical loop quantization

Spin foam models are usually defined over a given discretization of spacetime. This contrast with canonical loop quantized theories, which are "diffeomorphism" covariant, is overcome in a natural way when the canonical framework is defined as a projective limit organizing the information contained in embedded discrete theories; the missing piece is the appropriate framework to organize the information contained in collections of spin foam models. This formalism is introduced in the article

Continuum spin foam model for 3-d gravity
Jose A. Zapata, J.Math.Phys. 43 (2002) 5612-5623

After the general formalism is developed, it is applied to the case of 3d gravity. In this case the limits involved in the definition of the theory in the continuum converge rather trivially, but the structure that can manage more complex situations is, in principle, given.

A more compact exposition of the formalism is presented in a short article that has the objective of presenting loop quantization (covariant and canonical) as the continuum limit of lattice gauge theory.

Loop quantization from a lattice gauge theory perspective
Jose A. Zapata, Class.Quant.Grav. 21 (2004) L115-L122

The article presents a critical view of loop quantization, and highlights issues that need to be addressed to construct non trivial loop quantized theories. For a description see the section "Renormalization tailored to loop quantization."