In this talk, I will introduce a model of quantum mechanics based on the theory of groupoids. I will show how one can construct a 2-groupid from Schwinger's algebra of so-called "selective measurements". We will look at some examples and see how one can recover the standard Hilbert space picture of quantum mechanics.
Groupoids and Schwinger's picture of quantum mechanics
Sep. 21, 2022 4:40pm (MATH 3…
Grad Student Seminar
Nick Jamesson (CU Boulder)
X
What does the formal study of logic look like? This is not an uncommon question for mathematicians who work outside of logic to have. We will shed some light on this question by looking at model theory, a branch of logic that deals with models, which can be thought of as "possible worlds where a set of sentences are true." For instance, the integers mod 2 are a model in which the sentence "1+1=0" is true. Since logic is known for theorems that sound cool (think Gödel's incompleteness theorems) we will prove a few basic statements that sound cool using a powerful tool, the compactness theorem for first order logic. We'll also apply the compactness theorem to regular old math to give a model theoretic proof that every field is contained in an algebraically closed field.
Demystifying Logic: A Crash Course in Model Theory