Abstract
We study various properties of a Proca field coupled to gravity through minimal and quadrupole interactions, described by a two-parameter family of Lagrangians. Stückelberg decomposition of the effective theory spells out its model-dependent ultraviolet cutoff, parametrically larger than the Proca mass. We present pp-wave solutions that the model admits, consider linear fluctuations on such backgrounds, and thereby constrain the parameter space of the theory by requiring null-energy condition and the absence of negative time delays in high-energy scattering. We briefly discuss the positivity constraints—derived from unitarity and analyticity of scattering amplitudes—that become ineffective in this regard.
Highlights
Fundamental particles relevant to our world must interact with gravity because of its universal nature
When it comes to massive particles of low spin, such as the Proca field, there seem to be no issues with coupling to gravity
Non-minimal couplings to the Ricci tensor and the scalar curvature do appear in our action (1) but they result in trivial cubic interactions in flat space
Summary
Fundamental particles relevant to our world must interact with gravity because of its universal nature. What makes even a fundamental particle behave like an extended object sensitive to tidal forces is its non-zero Compton wavelength, which sets an intrinsic size When it comes to massive particles of low spin, such as the Proca field, there seem to be no issues with coupling to gravity. Non-minimal couplings to the Ricci tensor and the scalar curvature do appear in our action (1) but they result in trivial cubic interactions in flat space. This gives a model-dependent effective field theory cutoff.
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