PIRSA:19110054

Minimum length scenarios that maintain continuous symmetries

APA

Pye, J. (2019). Minimum length scenarios that maintain continuous symmetries. Perimeter Institute for Theoretical Physics. https://pirsa.org/19110054

MLA

Pye, Jason. Minimum length scenarios that maintain continuous symmetries. Perimeter Institute for Theoretical Physics, Nov. 07, 2019, https://pirsa.org/19110054

BibTex

          @misc{ scivideos_PIRSA:19110054,
            doi = {10.48660/19110054},
            url = {https://pirsa.org/19110054},
            author = {Pye, Jason},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Minimum length scenarios that maintain continuous symmetries},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2019},
            month = {nov},
            note = {PIRSA:19110054 see, \url{https://scivideos.org/pirsa/19110054}}
          }
          

Jason Pye Nordic Institute for Theoretical Physics

Talk numberPIRSA:19110054
Source RepositoryPIRSA
Collection

Abstract

It has long been argued that combining the uncertainty principle with gravity will lead to an effective minimum length at the Planck scale. A particular challenge is to model the presence of a smallest length scale in a manner which respects continuous spacetime symmetries. One path for deriving low-energy descriptions of an invariant minimum length in quantum field theory is based on generalized uncertainty principles. Here I will consider the question how this approach enables one to retain Euclidean or even Lorentzian symmetries. The Euclidean case yields a ultraviolet cutoff in the form of a bandlimit, and this then allows one to apply the powerful Shannon sampling theorem of classical information theory which establishes the equivalence between continuous and discrete representations of information. As a consequence, one obtains discrete representations of fields which are more subtle than a simple discretization of space, and are in fact equivalent to a continuum representation. Quantum fields in this model exhibit a finite density of information and a corresponding regularization of the entanglement of the vacuum, as I will demonstrate in detail. We then examine the Lorentzian symmetry generalization. This case leads to a Lorentz-invariant analogue of bandlimitation, and we discuss the nature of the corresponding sampling theory.