2016/04/30 by Rabin Banerjee, Pradip Mukherjee · 3 citations
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Connection (principal bundle) #Cosmology and Gravitation Theories #Expression (computer science) #Galilean #Gauge theory #Minimal coupling #Scalar (mathematics) #Scalar field #Spacetime #Torsion (gastropod) #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/33/22/225013
published as Class. Quantum Grav. 33 225013 2016 · 21 pages, latex, journal version
openalex created_date 2016/06/24 · openalex publication_date 2016/10/26 · arxiv created 2016/11/02 · arxiv updated 2016/11/03 · openalex updated_date 2026/08/05
Using the recently advanced Galilean gauge theory (GGT) we give a comprehensive construction of torsional Newton–Cartan (NC) geometry. The coupling of a Galilean symmetric model with background NC geometry following GGT is illustrated by a free nonrelativistic scalar field theory. The issue of spatial diffeomorphism (Son and Wingate 2006 Ann. Phys. 321 197–224 ; Banerjee et al 2015 Phys. Rev. D 91 084021 ) is focussed from a new angle. The expression of the torsionful connection is worked out, which is in complete parallel with the relativistic theory. Also, smooth transition of the connection to its well known torsionless expression is demonstrated. A complete (implicit) expression of the torsion tensor for the NC spacetime is provided where the first-order variables occur in a suggestive way. The well known result for the temporal part of torsion is reproduced from our expression.