Jason Pye , Applied Mathematics, University of Waterloo
On a Covariant Minimum Length for Quantum Field Theory
It has long been speculated that gravity may induce an effective minimum length in nature. It has also been entertained that such minimum length scale may provide a regulator for the many ultraviolet divergences that plague quantum field theory. Such a fundamental length scale is also an important ingredient in some approaches to quantum gravity. However, an issue with many models of such a minimum length scale is that they break the Lorentz symmetry of relativistic quantum field theories, which can lead to pathological behaviour of the theory not observed in nature.
Here we examine a model for a covariant version of a minimum length by introducing a covariant extension of the generalised uncertainty principle to quantum field theory. We find that it implies the theory will have a kind of covariant bandlimitation which cuts off quantum fluctuations near the minimum length scale. We then proceed to study the effect of this bandlimitation on flat and curved spacetimes, as well as consider to the implications for the gauge principle, interactions, as well as possible detection.