https://doi.org/10.1140/epjp/s13360-025-06009-5
Regular Article
Covariant operator formalism for higher derivative systems: vector spin-0 dual model as a prelude to generalized QED
1
Physics Department, Federal University of the Triângulo Mineiro UFTM, 38025-180, Uberaba, MG, Brazil
2
Institute of Exact Sciences, Federal University of Alfenas UNIFAL, 37133-840, Alfenas, MG, Brazil
3
Institute of Physics and Chemistry, Federal University of Itajubá UNIFEI, 37500-903, Itajubá, MG, Brazil
Received:
18
October
2024
Accepted:
11
January
2025
Published online:
24
January
2025
In this work, we extend the Kugo–Ojima–Nakanishi covariant operator formalism to quantize two higher derivative systems, considering their extended phase space structures, more specifically, the one describing spin-0 particles by a vector field and the generalized electrodynamics. We investigate the commutator structure of these theories and present the definition of their physical Hilbert subspaces. The first model presents a reducible gauge symmetry, implying the necessity of two sets of auxiliary fields. The massless limit is also carefully analyzed. After this prelude, the generalized QED can be investigated with such machinery. Regarding the interacting regime, the positive norm subspace is no longer time invariant, since the interaction can create negative norm states from an initially ghost-free one. Then, we furnish an alternative description of the situation by analyzing a set of spectral representations highlighting the lack of positivity associated with the well-known ultraviolet improvement. Finally, based on these efforts and also on recent discussions about Lee–Wick-like models, we prove that it is possible to establish a specific higher derivative interacting model compatible with establishing a time-invariant positive norm subspace.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
