2016/09/30 by Nayem Sk, Nayem Sk., Abhik Kumar Sanyal
Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal map #Cosmology and Gravitation Theories #Diffeomorphism #Equivalence (formal languages) #General covariance #Hamiltonian (control theory) #Homogeneous space #Mathematical structure #Noether's theorem #Noncommutative and Quantum Gravity Theories #Quantum #Quantum field theory #Quantum gravity #gr-qc
paper · pdf · doi:10.1142/s0218271817501620
published as IJMPD, Vol. 26 (2017) 1750162 (18 pages) · 14 pages, To appear in IJMPD (2017)
openalex created_date 2016/09/23 · arxiv created 2017/08/01 · arxiv updated 2017/08/02 · openalex publication_date 2017/08/11 · openalex updated_date 2026/08/05
Whether Jordan’s and Einstein’s frame descriptions of [Formula: see text] theory of gravity are physically equivalent, is a long standing debate. However, practically none questioned on true mathematical equivalence, since classical field equations may be translated from one frame to the other following a transformation relation. Here, we show that, neither Noether symmetries, Noether equations, nor may quantum equations be translated from one to the other. The reason being, — conformal transformation results in a completely different system, with a different Lagrangian. Field equations match only due to the presence of diffeomorphic invariance. Unless a symmetry generator is found which involves Hamiltonian constraint equation, mathematical equivalence between the two frames appears to be vulnerable. In any case, in quantum domain, mathematical and therefore physical equivalence cannot be established.