https://doi.org/10.1140/epjp/s13360-024-05837-1
Regular Article
Infinite derivative theories and equations
1
School of Physical Sciences and Technology, ShanghaiTech University, Huanke rd, 199, 201210, Shanghai, China
2
Departamento de Física, Centro de Matemática e Aplicaçoes (CMA-UBI), Universidade da Beira Interior, Rua Avila e Bolama, 6200, Covilhã, Portugal
a
askoshelev@shanghaitech.edu.cn
Received:
4
September
2024
Accepted:
12
November
2024
Published online:
12
December
2024
In this note we would like to reiterate in a concise manner different mathematical aspects of equations with infinite derivatives appearing in analytic infinite derivative scalar and gravitational theories. Namely, we discuss (i) an appearance of ghosts even if a ghost-free condition is fixed, (ii) background dependence of the presence of ghosts in an infinite derivative gravity (iii) different approaches to studying corresponding equations of motion including analysis of stability and proofs of uniqueness of solutions. We also demonstrate how an analysis of the spectrum of physical excitations in an infinite derivative gravity helps reducing the number of independent higher derivative operators.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024
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.
