On the Application of Bandlimitation and Sampling Theory to Quantum Field Theory
Abstract
It is widely believed that combining the uncertainty principle with gravity will lead to an effective minimum length scale. A particular challenge is to specify this scale in a coordinate-independent manner so that covariance is not broken. Here we will consider bandlimitation and sampling theory as a means to model Planck-scale modifications to spacetime within quantum field theory. Two different cases will be considered.
The first is the case of Euclidean-bandlimitation, which imposes a notion of minimal length while preserving Euclidean symmetries. This leads to a sampling theory where one can represent fields as equivalently living on either continuous space or on lattices. We will discuss how this leads to a regulation of the information density in quantum fields. We then proceed to quantify notions of localization and density of degrees of freedom within these fields.
We then turn to the case of Lorentzian-bandlimitation. Quantum fields bandlimited in this way have reconstruction properties which are qualitatively different than the Euclidean case. Nevertheless, here we will examine what impacts this has on the structure of quantum field theory with such a bandlimit imposed. In particular, we will investigate which quantities are and are not regulated by the Lorentzian bandlimit in both free and interacting field theories.
Collections
Cite this version of the work
Jason Pye
(2020).
On the Application of Bandlimitation and Sampling Theory to Quantum Field Theory. UWSpace.
http://hdl.handle.net/10012/16427
Other formats
Related items
Showing items related by title, author, creator and subject.
-
Holographic Experiments on Defects
Wapler, Matthias Christian (University of Waterloo, 2009-09-03)Using the AdS/CFT correspondence, we study the anisotropic transport properties of both supersymmetric and non-supersymmetric matter fields on (2+1)-dimensional defects coupled to a (3+1)-dimensional N=4 SYM "heat bath". ... -
Impact of a University Environmental Sustainability Strategy on Employees
Westwood, Ray (University of Waterloo, 2020-08-27)The ever-growing trend of campus sustainability, coupled with pressure from external stakeholders (competitor actions, government regulations, etc.) induces organizations to adopt sustainability and its triple bottom line ... -
Matrix analytic methods for computations in risk theory
Kim, Sung Soo (University of Waterloo, 2019-01-15)The introduction of matrix analytic methods in risk theory has marked a significant progress in computations in risk theory. Matrix analytic methods have proven to be powerful computational tools for numerically analyzing ...