Why surplus structure is not superfluous
History and Philosophy of Physics
2017-12-05 v1 Mathematical Physics
math.MP
Abstract
The idea that gauge theory has 'surplus' structure poses a puzzle: in one much discussed sense, this structure is redundant; but on the other hand, it is also widely held to play an essential role in the theory. In this paper, we employ category-theoretic tools to illuminate an aspect of this puzzle. We precisify what is meant by 'surplus' structure by means of functorial comparisons with equivalence classes of gauge fields, and then show that such structure is essential for any theory that represents a rich collection of physically relevant fields which are 'local' in nature.
Keywords
Cite
@article{arxiv.1712.01228,
title = {Why surplus structure is not superfluous},
author = {James Nguyen and Nicholas J. Teh and Laura Wells},
journal= {arXiv preprint arXiv:1712.01228},
year = {2017}
}