2021/10/14 by Henrique Gomes, Gomes, Henrique
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #History and Philosophy of Physics (physics.hist-ph) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2110.07203
openalex publication_date 2021/10/14 · openalex created_date 2022/11/03 · openalex updated_date 2026/07/28
The following questions are germane to our understanding of gauge-(in)variant quantities and physical possibility: how are gauge transformations and spacetime diffeomorphisms understood as symmetries, in which ways are they similar, and in which are they different? To what extent are we justified in endorsing different attitudes -- nowadays called sophistication, haecceitism, and eliminativism -- towards each? This is the first of four papers taking up this question. This first paper will discuss notions of symmetries and isomorphisms that will be used in the remaining papers in the series. There are several such notions in the literature and the question of how they mesh with empirical discernibility is a delicate one; even the orthodox view that symmetries are empirically unobservable (even in principle) has recently been challenged by Belot. Focusing on local field theories, I will provide a precise definition of dynamical symmetries in terms of the space of states of the theory at hand. I will then apply the definition to Yang-Mills theories and general relativity and show that these symmetries correspond to automorphisms of `natural' geometric structures: the small diffeomorphisms of the spacetime manifold and the small fiber-preserving diffeomorphisms of a fibered space. Finally, I will show that these automorphisms can be given a passive gloss, since they correspond 1-1 to the coordinate transformations of the underlying manifolds.