2012/11/30 by Xiao Liu, Fei Huang, Jian-Yang Zhu · 4 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology #Cosmology and Gravitation Theories #Geometry #Isotropy #Loop quantum cosmology #Loop quantum gravity #Massless particle #Mathematical physics #Noncommutative and Quantum Gravity Theories #Path integral formulation #Physics #Quantum #Quantum cosmology #Quantum gravity #Quantum mechanics #Scalar (mathematics) #Scalar field #Spin foam #Theoretical physics #Yukawa potential #gr-qc
paper · pdf · doi:10.1088/0264-9381/30/6/065010
published in Classical and Quantum Gravity 30(6), 065010 (IOP Publishing) · 11 pages,revised version, accepted for publication in Class. Quantum Grav
arxiv created 2013/02/01 · openalex publication_date 2013/02/21 · arxiv updated 2015/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A path integral formulation of the Bianchi I models containing a massless scalar field in loop quantum cosmology is constructed. Following the strategy used in the homogenous and isotropic case, the calculation is extended to the simplest non-isotropic models according to the μ and μ′ scheme. It is proved from the path integral angle that the quantum dynamic lacks the full invariance with respect to fiducial cell scaling in the μ scheme, but it does not in the μ′ scheme. The investigation affirms the equivalence of the canonical approach and the path integral approach in loop quantum cosmology.