Speaker
Description
Canonical Quantum Mechanics (CQM) is performed on a vector space over either the Field of Real or Complex numbers, and is equipped with an inner product, particularly a Hermitian form. This allows for a rich and experimentally verified model of non-relativistic physics on the smallest physically relevant scale. Questions have been raised however about whether the theory is obscuring a deep more fundamental problem. One way to refer to this problem is “too complete.” This presentation will demonstrate how replacing the Real and Complex numbers with extensions of Finite Fields leads to a similar but simpler mathematical object on which quantum calculations can be performed. This model is called “Galois Field Quantum Mechanics” or GFQM. Important operations within CQM are shown to have analogous objects within GFQM and what role they serve in the model is elaborated on. Applications of the theory are discussed. For example, a special case appears within the case of Mutually Unbiased Bases. Potential avenues for further research are suggested.
