2021/04/11 by Peter Woit, Woit, Peter · 1 citation
Engineering · #Advanced Measurement and Metrology Techniques #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Metal Forming Simulation Techniques #Metallurgy and Material Forming
paper · pdf · doi:10.48550/arxiv.2104.05099
openalex publication_date 2021/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Taking Euclidean signature space-time with its local Spin(4)=SU(2)xSU(2) group of space-time symmetries as fundamental, one can consistently gauge one SU(2) factor to get a chiral spin connection formulation of general relativity, the other to get part of the Standard Model gauge fields. Reconstructing a Lorentz signature theory requires introducing a degree of freedom specifying the imaginary time direction, which will play the role of the Higgs field. To make sense of this one needs to work with twistor geometry, which provides tautological spinor degrees of freedom and a framework for relating by analytic continuation spinors in Minkowski and Euclidean space-time. It also provides internal U(1) and SU(3) symmetries as well as a simple construction of the degrees of freedom of a Standard Model generation of matter fields. In this proposal the theory is naturally defined on projective twistor space rather than the usual space-time, so will require further development of a gauge theory and spinor field quantization formalism in that context.