Abstract
It has recently been argued that half degrees of freedom could emerge in Lorentz and parity invariant field theories, using a non-linear Proca field theory dubbed Proca-Nuevo as a specific example. We provide two proofs, using the Lagrangian and Hamiltonian pictures, that the theory possesses a pair of second class constraints, leaving D − 1 degrees of freedom in D spacetime dimensions, as befits a consistent Proca model. Our proofs are explicit and straightforward in two dimensions and we discuss how they generalize to an arbitrary number of dimensions. We also clarify why local Lorentz and parity invariant field theories cannot hold half degrees of freedom.
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Acknowledgments
CdR is supported by STFC Consolidated Grant ST/T000791/1 and a Simons Investigator award 690508. SGS acknowledges support from the NSFC Research Fund for International Scientists (Grant No. 12250410250). VP is funded by an Imperial College President’s Fellowship. LH is supported by funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme grant agreement No 801781 and by the Swiss National Science Foundation grant 179740. LH further acknowledges support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2181/1 - 390900948 (the Heidelberg STRUCTURES Excellence Cluster).
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de Rham, C., Garcia-Saenz, S., Heisenberg, L. et al. To Half-Be or Not To Be?. J. High Energ. Phys. 2023, 88 (2023). https://doi.org/10.1007/JHEP06(2023)088
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DOI: https://doi.org/10.1007/JHEP06(2023)088