2022/12/06 by J. Brian Pitts, Pitts, J. Brian · 2 citations
Arts and Humanities · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #History and Philosophy of Physics (physics.hist-ph) #Philosophy and History of Science #Quantum Mechanics and Applications #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2212.02944
openalex publication_date 2022/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently two pairs of authors have aimed to vindicate the longstanding conventional claim that a first-class constraint generates a gauge transformation in typical gauge theories such as electromagnetism, Yang-Mills and General Relativity, in response to the Lagrangian-equivalent reforming tradition, in particular Pitts, Annals of Physics_ 2014. Both pairs emphasize the coherence of the extended Hamiltonian formalism against what they take to be core ideas in Pitts 2014, but both overlook Pitts 2014's sensitivity to ways that one might rescue the claim in question, including an additive redefinition of the electrostatic potential. Hence the bulk of the paper is best interpreted as arguing that the longstanding claim about separate first-class constraints is either false or trivial_ -- de-Ockhamization (using more when less suffices by splitting one quantity into the sum of two) being trivial. Unfortunately section 9 of Pitts 2014, a primarily verbal argument that plays no role in other works, is refuted. Pooley and Wallace's inverse Legendre transformation to de-Ockhamized electromagnetism with an additively redefined electrostatic potential, however, opens the door to a precisely analogous calculation introducing a photon mass, which shows that a second-class primary_ constraint generates a gauge transformation in the exactly same sense -- a reductio ad absurdum of the claim that a first-class constraint generates a gauge transformation and a second-class constraint does not. Gauge freedom by de-Ockhamization does not require any constraints at all, first-class or second-class, because any dynamical variable in any Lagrangian can be de-Ockhamized into exhibiting trivial additive artificial gauge freedom by splitting one quantity into the sum of two. Physically interesting gauge freedom, however, is typically generated by a tuned sum of first-class constraints.