Year: 2025
Type: preprint
Abstract: We re-examine the derivation of the equations of motion from an action principle for classical field theories with non-holonomic constraints, \textit{i.e.}, constraints involving derivatives of the fields. We find that the usual method for gauge fixing in classical and quantum field theories is highly non-trivial for non-holonomic gauge constraints, such as the Coulomb and Lorenz gauges. The subtlety appears at the use of the so-called transposition rule, $δ(\partial_νA^μ)=\partial_ν(δA^μ)$, which has been shown not to hold for general non-holonomic constraints in the point-particle context. We provide a sufficient definition of integrable non-holonomic constraints in classical field theory that allows us to prove that the transposition rule holds for all theories with these constraints; we are then able to recover the usual treatment of gauge fixing for gauges of this type.
Source: arXiv (Cornell University)
Authors: Bert, Ben, Horowitz, William A.
Institutions: University of Cape Town, New Mexico State University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: CERN, National Research Foundation
OpenAlex ID: W4415036097
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