The equivalence theorem in the generalized gravity of f(R)-type and canonical quantization II
Abstract
We first review the equivalence theorem of the f(R)-type gravity to Einstein gravity with a scalar field by deriving it in a self-contained and pedagogical way. Then we describe the problem of to what extent the equivalence holds. Main problems are (i) Is the surface term given by Gibbons and Hawking which is necessary in Einstein gravity also necessary in the f(R)-type gravity? (ii) Does the equivalence hold also in quantum theory? (iii) Which metric is physical, i.e., which metric should be identified with the observed one? In this work, we clarify the problem (i) and review the problem (ii) in a canonical formalism which is the generalization of the Ostrogradski one. We briefly comment on the problem (iii). Some discussions are given on one of the results of (ii) concerning the general relativity in non-commutative spacetime.
Keywords
Cite
@article{arxiv.1204.2396,
title = {The equivalence theorem in the generalized gravity of f(R)-type and canonical quantization II},
author = {Yasuo Ezawa and Yoshiaki Ohkuwa},
journal= {arXiv preprint arXiv:1204.2396},
year = {2015}
}
Comments
23 pages. Ecept for the change of style from {book} to {article} and related changes, e.g., addition of abstract and the form of References, as well as the addition of Appendix B, the work has been published as one of the chapters in the book "Advances in Quantum Theory" (2012, ed. Ion I. Cotaescu; InTech Open Access Publisher)