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Higher derivative scalar-tensor monomials and their classification

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Abstract

We make a full classification of scalar monomials built of the Riemann curvature tensor up to the quadratic order and of the covariant derivatives of the scalar field up to the third order. From the point of view of the effective field theory, the third or even higher order covariant derivatives of the scalar field are of the same importance as the higher curvature terms, and thus should be taken into account. Moreover, the higher curvature terms and the higher order derivatives of the scalar field are complementary to each other, of which novel ghostfree combinations may exist. We make a systematic classification of all the possible monomials, according to the numbers of the Riemann tensor and the higher derivatives of the scalar field in each monomial. A complete basis of monomials at each order is derived, of which the linear combinations may yield novel ghostfree Lagrangians. We also develop diagrammatic representations for the monomials, which may help to simplify the analysis.

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Authors and Affiliations

  1. School of Physics and Astronomy, Sun Yat-sen University, Guangzhou, 510275, China

    Xian Gao

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  1. Xian Gao
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Correspondence to Xian Gao.

Additional information

I would like to thank M. Crisostomi for the discussion. This work was supported by the National Natural Science Foundation of China (Grant No. 11975020).

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Gao, X. Higher derivative scalar-tensor monomials and their classification. Sci. China Phys. Mech. Astron. 64, 210012 (2021). https://doi.org/10.1007/s11433-020-1607-3

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  • DOI: https://doi.org/10.1007/s11433-020-1607-3

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