6533b830fe1ef96bd12972fc
RESEARCH PRODUCT
General invertible transformation and physical degrees of freedom
Tsutomu KobayashiHayato MotohashiHayato MotohashiTeruaki SuyamaKazufumi Takahashisubject
High Energy Physics - TheoryPhysicsPure mathematicsCosmology and Nongalactic Astrophysics (astro-ph.CO)010308 nuclear & particles physicsEquations of motionMaterial derivativeClassical Physics (physics.class-ph)FOS: Physical sciencesPhysics - Classical PhysicsGeneral Relativity and Quantum Cosmology (gr-qc)01 natural sciencesGeneral Relativity and Quantum CosmologyTensor fieldlaw.inventionField transformationInvertible matrixHigh Energy Physics - Theory (hep-th)law0103 physical sciencesEquivalence (formal languages)010306 general physicsField equationScalar fieldAstrophysics - Cosmology and Nongalactic Astrophysicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-04-27 |