Abstract
We study the aspects of constructing the interactions for the higher spin fields in the framework of BRST approach. The main object of such an approach is BRST operator acting in the appropriate Fock space and building on the base of constraints that define the irreducible higher spin representations. In its turn, the constraints are divided into differential and purely algebraic or holonomic. The necessary and sufficient conditions to derive the consistent Lagrangian formulations for irreducible interacting higher-spin fields within approach with incomplete BRST operator, where the algebraic constraints are not included into definition of the BRST operator but imposed ad hoc on the field and gauge parameter vectors, are considered. It is shown that in addition to that such constraints should (anti)commute with the BRST operator and annihilate the fields and gauge parameters Fock space vectors, they must form the Abelian (super)algebra both with the BRST operator above and with operators of cubic, quartic and etc. vertices. Only under the above conditions, the formulations with complete and incomplete BRST charges turn out to be equivalent and yield to the same interaction vertices in terms of irreducible fields.
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Notes
At present, there is an extensive literature devoted to the BRST approach for free fields of higher spins; here we only cite one of the first works in this direction.
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ACKNOWLEDGMENTS
The authors are grateful to organizers and participants of International Workshop “Supersymmetries and Quantum Symmetries 2022” for hospitality and useful discussions of the presented results.
Funding
The work was partially supported by the Ministry of Education of Russian Federation, project no. QZOY-2023-0003.
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Buchbinder, I.L., Reshetnyak, A.A. Consistent Lagrangians for Irreducible Interacting Higher-Spin Fields with Holonomic Constraints. Phys. Part. Nuclei 54, 1066–1071 (2023). https://doi.org/10.1134/S1063779623060084
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DOI: https://doi.org/10.1134/S1063779623060084