Second-order scalar-tensor field equations in a four-dimensional space

@article{Horndeski1974SecondorderSF,
  title={Second-order scalar-tensor field equations in a four-dimensional space},
  author={Gregory W. Horndeski},
  journal={International Journal of Theoretical Physics},
  year={1974},
  volume={10},
  pages={363-384}
}
  • G. W. Horndeski
  • Published 1 September 1974
  • Mathematics
  • International Journal of Theoretical Physics
Lagrange scalar densities which are concomitants of a pseudo-Riemannian metric-tensor, a scalar field and their derivatives of arbitrary order are considered. The most general second-order Euler-Lagrange tensors derivable from such a Lagrangian in a four-dimensional space are constructed, and it is shown that these Euler-Lagrange tensors may be obtained from a Lagrangian which is at most of second order in the derivatives of the field functions. 
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