Action principle of Galilean relativistic Proca theory
arXiv:2303.13066 · doi:10.1140/epjc/s10052-023-12098-2
Abstract
In this paper, we discuss Galilean relativistic Proca theory in detail. We first provide a set of mapping relations, derived systematically, that connect the covariant and contravariant vectors in the Lorentz relativistic and Galilean relativistic formulations. Exploiting this map, we construct the two limits of Galilean relativistic Proca theory from usual Proca theory in the potential formalism for both contravariant and covariant vectors which are now distinct entities. An action formalism is thereby derived from which the field equations are obtained and their internal consistency is shown. Next we construct Noether currents and show their on-shell conservation. We introduce analogues of Maxwell's electric and magnetic fields and recast the entire analysis in terms of these fields. Explicit invariance under Galilean transformations is shown for both electric/magnetic limits. We then move to discuss Stuckelberg embedded Proca model in the Galilean framework.
16 pages, 3 tables, some comments added, matches with the published version
References in corpus (10)
- Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
- Revisiting non-relativistic limits
- A new formulation of non-relativistic diffeomorphism invariance
- Kerr black holes with synchronised Proca hair: lensing, shadows and EHT constraints
- Galilean Conformal Electrodynamics
- Impact of the wave-like nature of Proca stars on their gravitational-wave emission
- More On Nonrelativistic Diffeomorphism Invariance
- Geometric Proca with Matter in Metric-Palatini Gravity
- New formulation of Galilean relativistic Maxwell theory
- To Half--Be or Not To Be?