https://doi.org/10.1140/epjp/i2015-15077-5
Regular Article
On the canonical formalism of f(R)-type gravity using Lie derivatives
1
Section of Mathematical Science, Dept. of Social Medicine, Faculty of Medicine, University of Miyazaki, 889-1692, Kihara, Kiyotake-cho, Miyazaki, Japan
2
Dept. of Physics, Ehime University, 790-8577, Bunkyo-cho, Matsuyama, Japan
* e-mail: ohkuwa@med.miyazaki-u.ac.jp
Received:
25
December
2014
Revised:
12
March
2015
Accepted:
30
March
2015
Published online:
20
April
2015
We present a canonical formalism of the f(R)-type gravity using the Lie derivatives instead of the time derivatives by refining the formalism of our group. The previous formalism is a direct generalization of the Ostrogradski’s formalism. However the use of the Lie derivatives was not sufficient, in that Lie derivatives and time derivatives are used in a mixed way, so that the expressions are somewhat complicated. In this paper, we use the Lie derivatives and foliation structure of the spacetime thoroughly, which makes the procedure and the expressions far more concise.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2015
