https://doi.org/10.1140/epjp/s13360-023-04144-5
Regular Article
Generalized canonical approach to deformation problem in gauge theories
1
Center of Theoretical Physics, Tomsk State Pedagogical University, Kievskaya St. 60, 634061, Tomsk, Russia
2
Bogoliubov Laboratory of Theoretical Physics, JINR, 141980, Dubna, Moscow Region, Russia
3
National Research Tomsk State University, Lenin Av. 36, 634050, Tomsk, Russia
Received:
1
March
2023
Accepted:
26
May
2023
Published online:
9
June
2023
We develop a general approach to constructing a deformation that describes the mapping of any dynamical system with irreducible first-class constraints in the phase space into another dynamical system with first-class constraints. It is shown that such a deformation problem can be efficiently explored in the framework of the Batalin–Fradkin–Vilkovisky (BFV) formalism. The basic objects of this formalism are the BRST-BFV charge and a generalized Hamiltonian that satisfy the defining equations in the extended phase space in terms of (super)Poisson brackets. General solution to the deformation problem is found in terms of a (super)canonical transformation with a special generating function which is explicitly established. It is proved that this generating function is determined by a single arbitrary function which depends only on coordinates of initial dynamical system. In general, such a function must be non-local, but the deformed theory may nevertheless have a local sector. To illustrate the developed approach, we have constructed a non-local deformation of the Abelian gauge theory into a non-local non-Abelian gauge theory whose local sector coincides with the standard Yang–Mills theory.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. 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.
