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On constrained analysis and diffeomorphism invariance of generalised Proca theories

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Abstract

We consider a whole class of theories, each of which describes dynamics of a vector field coupled to any external background field. Furthermore, each of these theories is diffeomorphism invariance, has time–time and time-space components of Hessian of the vector sector equal zero but with space–space part being non-degenerate, and the vector sector is free from Ostrogradski instability. By using the Faddeev–Jackiw constrained analysis, we derive the conditions that theories in this class have to satisfy in order for the vector sector to have \(d-1\) propagating degrees of freedom in \(d\)-dimensional spacetime. Most of these conditions are trivialised due to diffeomorphism invariance requirements. This leaves only a condition that a complicated combination of terms should not be trivially zero. Being an inequality, this condition is naturally easy to be fulfilled. We verify our result by using the Dirac constrained analysis to obtain the same result. Furthermore, we have also made a small remark on how the absence of diffeomorphism invariance affects the form of Faddeev–Jackiw brackets.

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Acknowledgements

We are grateful to Sheng-Lan Ko for interests, helpful discussions, and various comments on the manuscript. We would also like to thank Lavinia Heisenberg, Yeinzon Rodriguez, and Christian Steinwachs for interests and comments. Furthermore, we thank anonymous referees for helpful comments which improve our manuscript. J.S. is supported by an IF Scholarship from the Institute for Fundamental Study “The Tah Poe Academia Institute”, Naresuan University, and a Research Grant for Graduate Student from the Graduate School, Naresuan University. P.V. thanks University of Phayao, and Rajamangala University of Technology Suvarnabhumi for hospitality, where part of this work was carried out.

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  1. The Institute for Fundamental Study “The Tah Poe Academia Institute”, Naresuan University, Phitsanulok-Nakhonsawan Road, Phitsanulok, 65000, Thailand

    Jarunee Sanongkhun & Pichet Vanichchapongjaroen

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  1. Jarunee Sanongkhun
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  2. Pichet Vanichchapongjaroen
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Correspondence to Pichet Vanichchapongjaroen.

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Sanongkhun, J., Vanichchapongjaroen, P. On constrained analysis and diffeomorphism invariance of generalised Proca theories. Gen Relativ Gravit 52, 26 (2020). https://doi.org/10.1007/s10714-020-02678-y

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