The Lattice-Continuum Correspondence in Quantum Mechanics

Abstract: It is very well known that long-distance correlation functions of many lattice systems can be calculated from continuum QFTs. Making this correspondence more precise --- identifying continuum operators that correspond to individual lattice operators, or exhibiting the lattice origins of subtler continuum phenomena like operator product expansions --- has proven quite daunting. In this talk, I will report on recent progress in this direction, using quantum mechanics (QFT in 0+1 dimensions) as an example. I will show how a finite but large quantum system can be systematically reduced to an Ersatz continuum theory, using both Hamiltonian and path integral formalisms. Along the way I will point out the lattice origins of several familiar continuum concepts, including contact terms, scale invariance, and the distinction between compact and noncompact theories. I will also stress the limitations imposed on the emergent continuum theory by its lattice progenitor --- for instance, any supersymmetric continuum theory emerging from a finite theory must have a vanishing Witten index.

differential geometrymetric geometry

Audience: researchers in the discipline

Western Hemisphere colloquium on geometry and physics

Series comments: Description: Biweekly colloquium of geometers and physicists

This weekly online colloquium features geometers and physicists presenting current research on a wide range of topics in the interface of the two fields. The talks are aimed at a broad audience. They will take place via Zoom on alternate Mondays at 3pm Eastern, noon Pacific, 4pm BRT. Each session features a 60 minute talk, followed by 15 minutes for questions and discussion. You may join the meeting 15 minutes in advance. Questions and comments may be submitted to the moderator via the chat interface during the talk, or presented in person during the Q&A session. These colloquia will be recorded and will be available (linked from the website) asap after the event.