2021/05/24 by Rabin Banerjee · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Consistency (knowledge bases) #Cosmology and Gravitation Theories #Covariant transformation #Gauge (firearms) #Gauge theory #Geometry #Gravitation #Mathematical physics #Mathematics #Newtonian dynamics #Newtonian fluid #Noncommutative and Quantum Gravity Theories #Physics #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.103.125009
published in Physical review. D/Physical review. D. 103(12) (American Physical Society) · 21 pages, No figures, Accepted in Physical Review D
arxiv created 2021/05/24 · openalex created_date 2021/06/07 · openalex publication_date 2021/06/10 · arxiv updated 2021/06/16 · openalex updated_date 2026/08/05
A covariant formulation for the Newton-Hooke particle is presented by following an algorithm developed by us R. Banerjee et al. [Phys. Lett. B 737, 369 (2014); Classical Quantum Gravity 32, 045010 (2015); Phys. Rev. D 91, 084021 (2015)]. It naturally leads to a coupling with the Newton-Cartan geometry. From this result we provide an understanding of gravitation in a Newtonian geometric background. Using Dirac's constrained analysis a canonical formulation for the Newton-Hooke covariant action is done in both gauge independent and gauge fixed approaches. While the former helps in identifying the various symmetries of the model, the latter is able to define the physical variables. From this analysis a path to canonical quantization is traced and the Schroedinger equation is derived which is shown to satisfy various consistency checks. Some consequences of this equation are briefly mentioned.