2013/01/25 by Claus Gerhardt, Gerhardt, Claus
Mathematics · Physics and Astronomy · #83 #83C #83C45 #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th #math-ph #math.DG #math.MP #msc:83 #msc:83C #msc:83C45
paper · pdf · doi:10.48550/arxiv.1301.6101
30 pages, v5: Redefined the Hilbert space in the CAR representation
openalex publication_date 2013/01/25 · arxiv created 2014/03/24 · arxiv updated 2014/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We quantize the interaction of gravity with Yang-Mills and spinor fields, hence offering a quantum theory incorporating all four fundamental forces of nature. Using canonical quantization we obtain solutions of the Wheeler-DeWitt equation in a vector bundle and the method of second quantization leads to a symplectic vector space (V,\om) and a corresponding CCR representation for the bosonic components and a CAR representation for the fermionic part. The solution space of the Wheeler-DeWitt equation is invariant under gauge transformations and under isometries in the spacelike base space \so of a given Riemannian metric ρij. We also define a net of local subalgebras which satisfy four of the Haag-Kastler axioms.