Derivative self-interactions for a massive vector field

By J. Jim'enez, Lavinia Heisenberg. 2016

218 citations recorded by the source corpus.

Abstract In this work we revisit the construction of theories for a massive vector field with derivative self-interactions such that only the 3 desired polarizations corresponding to a Proca field propagate. We start from the decoupling limit by constructing healthy interactions containing second derivatives of the Stueckelberg field with itself and also with the transverse modes. The resulting interactions can then be straightforwardly generalized beyond the decoupling limit. We then proceed to a systematic construction of the interactions by using the Levi–Civita tensors. Both approaches lead to a finite family of allowed derivative self-interactions for the Proca field. This construction allows us to show that some higher order terms recently introduced as new interactions trivialize in 4 dimensions by virtue of the Cayley–Hamilton theorem. Moreover, we discuss how the resulting derivative interactions can be written in a compact determinantal form, which can also be regarded as a generalization of the Born-Infeld lagrangian for electromagnetism. Finally, we generalize our results for a curved background and give the necessary non-minimal couplings guaranteeing that no additional polarizations propagate even in the presence of gravity.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/deda5c59460bb28e43e084c993e2eb2171830c5f

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Citations in the corpus

A systematic approach to generalisations of General Relativity and their cosmological implications (2018, methodology): “would vanish in four dimensions by the virtue of the Cayley-Hamilton theorem applied on Fν and, hence, such interactions trivialise in four dimensions [66].”
Generalization of the Proca Action (2014, methodology): “The fifth order interaction F̃F̃ μ∇αAβ does not need any non-minimal coupling on curved backgrounds in order to compensate higher order equations of motion [11, 12], unless the sixth order Lagrangian F̃F̃ ∇αAμ∇βAν [12], which requires the relative tuning with the non-minimal coupling between the fie”
Cosmology in generalized Proca theories (2016, background): “Finally, we would like to point out that there might be interesting consequences in the presence of the sixth-order interactions L6 = G6(X)L∇μAν∇αAβ+ G6,X(X)F̃ F̃∇αAμ∇βAν/2 [80, 81], where Lμναβ is the double dual Riemann tensor and F̃μν is the dual of the strength tensor.”
Generalized Proca action for an Abelian vector field (2015, methodology): “[37] for the parity-conserving sector, and by the present paper in the parity-violating sector, did not find any term other than those shown above up to the orders of L6 (parity violating) and L7 (parity conserving).”
Stellar structure models in modified theories of gravity: Lessons and challenges (2019, background): “The set of Lagrangians Li is characterized by several independent functions {G2,G3,G4,G5,G6,G7} which, in general, depend on both the vector potential and the field strength tensor (see [294, 295] for details).”