2017/12/04 by James Nguyen, Nguyen, James, Nicholas J. Teh +3 · 3 citations
Mathematics · Physics and Astronomy · #FOS: Physical sciences #History and Philosophy of Physics (physics.hist-ph) #Mathematical Physics (math-ph) #math-ph #math.MP #physics.hist-ph
paper · pdf · doi:10.48550/arxiv.1712.01228
arxiv created 2017/12/04 · arxiv updated 2017/12/05
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.