TY  - JOUR
AU  - Takahashi, K.
AU  - Motohashi, H.
AU  - Suyama, T.
AU  - Kobayashi, T.
PY  - 2017
DA  - 2017//
TI  - General invertible transformation and physical degrees of freedom
T2  - Phys. Rev. D
JO  - Physical Review D
SP  - 084053
EP  - 12pp
VL  - 95
IS  - 8
PB  - Amer Physical Soc
AB  - An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However, if the transformation depends on field derivatives, the equivalence between the two systems is nontrivial due to the appearance of higher derivative terms in the equations of motion. To address this problem, we prove the following theorem on the relation between an invertible transformation and Euler-Lagrange equations: If the field transformation is invertible, then any solution of the original set of Euler-Lagrange equations is mapped to a solution of the new set of Euler-Lagrange equations, and vice versa. We also present applications of the theorem to scalar-tensor theories.
SN  - 2470-0010
UR  - http://arxiv.org/abs/1702.01849
UR  - https://doi.org/10.1103/PhysRevD.95.084053
DO  - 10.1103/PhysRevD.95.084053
LA  - English
N1  - WOS:000400142700009
ID  - Takahashi_etal2017
ER  -