Abstracts Physics

Determining a minimal length scale for quantum gravity via commutators and modified operators

by Joey Contreras

Quantizing gravity has been one of the most difficult ventures in modern physics. There are several candidate theories for this issue such as loop quantum gravity, string theory, and the subject of this thesis, generalized uncertainty principle (GUP). Such theories postulate the existence of a minimal length or minimum possible resolution of the wave function on a Minkowski manifold. The question becomes how does one calculate this minimal length and also how does one test for it? The research presented in this thesis seeks to accomplish this by focusing on how the standard commutation relationship between position and momentum changes as the operators are modified. Additionally, this method avoids some of the constraints commonly associated with determining a minimal length scale.