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Intrinsically-defined higher-derivative Carrollian scalar field theories without Ostrogradsky instability
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We derive the most generic Carrollian higher derivative free scalar field theory intrinsically on a Carrollian manifold. The solutions to these theories are massless free particles propagating with speeds depending on the coupling constants in the Lagrangian, thus, allowing interference solutions which are not allowed on a Lorentzian manifold. This demonstrates that the set of solutions to the Carrollian theories is much larger than that of their Lorentzian counterparts. We also show that Carrollian higher derivative theories are more resistant to Ostrogradsky's instabilities. These instabilities can be resolved by choosing the coupling constants appropriately in the Carrollian Lagrangian, something that was proven to be impossible in Lorentzian theories.
Forward citations
Cited by 2 Pith papers
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Frozen Motion: Why Single Carrollian Scalars Cannot Propagate
Supertranslation invariance forces single minimally coupled Carrollian scalars to have static energy density and vanishing momentum density, precluding on-shell propagation.
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Higher-Order Newton-Cartan Gravity
The authors derive non-relativistic Newton-Cartan limits of quadratic gravity theories, obtaining higher-order corrected Poisson equations for Einstein-Gauss-Bonnet and Ricci-squared gravity.
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