Tuesday, November 8th

Mehdi Assanioussi, University of Warsaw

Matter in LQG
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by Jorge Pullin, LSU

Traditional quantum field theories are formulated using a mathematical framework called the Fock representation. In such mathematical framework physical elements like the notion of particles like photons and their properties have a well-defined mathematical counterpart. This framework is also used in quantum field theory in curved space-time, an approximation to full quantum gravity in which one treats gravity classically as a curved space-time and studies quantum fields that live on it. Quantum field theory in curved space-time has been extensively developed since the 1960’s and has led to major predictions like Hawking radiation or particle production in the early universe. If loop quantum gravity is to provide a good description of nature, one expects a connection of its framework with that of quantum field theory in curved space-time should emerge.

To this aim, Varadarajan, in the early years of this century, developed the r-Fock representation for quantum fields on flat and curved space-times. This representation has elements in common both with the loop representation used in loop quantum gravity and the Fock representation. At first it was only developed for Abelian quantum fields (like photons) and this was viewed as a limitation of the framework. Later, Ashtekar and Lewandowski presented a generalization to non-Abelian fields (like gluons), but it had some technical difficulties. The speaker, together with Lewandowski, has recently developed an alternative version of the r-Fock representation that bypasses the technical difficulties. The talk discussed this approach and outlined possibilities for it. Open questions include how to formulate the dynamics of loop quantum gravity in this representation and if it could help recover the continuum picture of classical space-time from the inherently discrete picture that loop quantum gravity yields at the quantum level.