Jason Pye, Applied Mathematics, University of Waterloo
Covariant Minimum Length in Quantum Field Theory
Many studies in quantum gravity indicate that physics should be nonlocal near the Planck scale. For instance, one model-independent feature seems to be that there should be a minimum length.
However, in the absence of a full theory of quantum gravity, one would like to understand how this nonlocality manifests itself in quantum field theory as we approach the Planck scale. It is of particular interest to develop a model for this nonlocality which preserves local Poincaré symmetry, and thus the causal structure of the theory.
Here we will discuss a model for a Poincaré-covariant minimum length based on deforming the commutation relations of the Heisenberg algebra. Topics that will be discussed in the context of this covariant minimum length include: the space of classical field configurations, quantisation of these fields, modification of the gauge principle, implementation of interactions between fields, as well as extensions to fields on curved spacetimes.