2016/04/30 by Javier Olmedo
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Degrees of freedom (physics and chemistry) #Equivalence (formal languages) #Heisenberg picture #Isotropy #Massless particle #Noncommutative and Quantum Gravity Theories #Observable #Scalar (mathematics) #Spacetime #gr-qc
paper · pdf · doi:10.1142/s0218271816420049
published as International Journal of Modern Physics D, 1642004 (2016) · 18 pages, minor corrections have been incorporated
openalex publication_date 2016/06/10 · arxiv created 2016/06/21 · arxiv updated 2016/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the relation between two evolution pictures that are currently considered for totally constrained theories. Both descriptions are based on Rovelli’s evolving constants approach, where one identifies a (possibly local) degree of freedom of the system as an internal time. This method is well understood classically in several situations. The purpose of this paper is to further analyze this approach at the quantum level. Concretely, we will compare the (Schrödinger-like) picture where the physical states evolve in time with the (Heisenberg-like) picture in which one defines parametrized observables (or evolving constants of the motion). We will show that in the particular situations considered in this paper (the parametrized relativistic particle and a spatially flat homogeneous and isotropic spacetime coupled to a massless scalar field) both descriptions are equivalent. We will finally comment on possible issues and on the genericness of the equivalence between both pictures.