2022-08-21   71852

Treating Space as a Lattice

Many introductions to quantum field theory (QFT) rely on perturbation theory – the art of using small-parameter expansions to approximate an exact expression – without ever clearly defining the exact expression in the first place. Everything in QFT makes more sense, both mathematically and physically, when we start with a nonperturbative definition instead. The only known nonperturbative constructions of many models involve at least temporarily replacing continuous space or spacetime with a discrete lattice. (This is clearly artificial, but that doesn't matter if the model isn't meant to be a Theory of Everything anyway.) This article introduces some basic concepts and conventions that several other articles in this series will use when defining QFTs on a spatial lattice.

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www.cphysics.org updated 2022-09-25