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The Riemann curvature tensor and Higgs scalar field within CAM theory. (English) Zbl 1437.81141

Summary: The composition algebra based methodology (CAM) [the author, Pap. Phys. 9, 090002 (2017); Phys Scr 94, No.2, Article ID 025301 (2019); Adv. Appl. Clifford Algebr. 27, No. 4, 3225–3234 (2017; Zbl 1379.81062);, J Appl Math Phys 6, No. 7, 1537–153, (2018; doi:10.4236/jamp.2018.67129); Phys Scr 94, No. 10, Article ID 105301 (2019)] has previously been shown to generate the pre-Higgs Standard Model Lagrangian. In this paper the symmetry of general covariance is incorporated into CAM. The Riemann curvature tensor thereby arises, from which gravity-field Lagrangians are constructed. A Higgs-like scalar field coupled to the spacetime metric tensor also manifests.

MSC:

81V22 Unified quantum theories
81R20 Covariant wave equations in quantum theory, relativistic quantum mechanics
83C47 Methods of quantum field theory in general relativity and gravitational theory
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
17A15 Noncommutative Jordan algebras
81V17 Gravitational interaction in quantum theory
70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
15A66 Clifford algebras, spinors

Citations:

Zbl 1379.81062
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