A metric-affine field model for the neutrino. (English) Zbl 1248.83008
Duplij, Steven (ed.) et al., Noncommutative structures in mathematics and physics. Dordrecht: Kluwer Academic Publishers (ISBN 0-7923-6998-X). NATO Sci. Ser. II, Math. Phys. Chem. 22, 427-439 (2001).
Summary: We construct our mathematical model for the neutrino as follows.
Firstly, we consider the Yang-Mills equation for the affine connection: \[ \delta_{\text{YM}}R=0\tag{1} \] where \(R\) is the Riemann curvature tensor and \(\delta_{\text{YM}}\) is the divergence on curvatures.
Secondly, we consider the Einstein equation:
\[ \text{Ric}=0\tag{2} \]
where Ric is the Ricci curvature tensor. Equation (2) describes the absence of sources of gravitation.
The objective of this paper is the study of the combined system (1), (2) which is a system of 80 real non-linear partial differential equations with 80 real unknowns \(g_{\mu\nu}\), \({\Gamma^\lambda}_{\mu\nu}\). In other words, we are combining the basic equation of relativistic quantum mechanics (Yang-Mills equation) with the basic equation of general relativity (Einstein equation).
For the entire collection see [Zbl 0964.00024].
Firstly, we consider the Yang-Mills equation for the affine connection: \[ \delta_{\text{YM}}R=0\tag{1} \] where \(R\) is the Riemann curvature tensor and \(\delta_{\text{YM}}\) is the divergence on curvatures.
Secondly, we consider the Einstein equation:
\[ \text{Ric}=0\tag{2} \]
where Ric is the Ricci curvature tensor. Equation (2) describes the absence of sources of gravitation.
The objective of this paper is the study of the combined system (1), (2) which is a system of 80 real non-linear partial differential equations with 80 real unknowns \(g_{\mu\nu}\), \({\Gamma^\lambda}_{\mu\nu}\). In other words, we are combining the basic equation of relativistic quantum mechanics (Yang-Mills equation) with the basic equation of general relativity (Einstein equation).
For the entire collection see [Zbl 0964.00024].
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 53C80 | Applications of global differential geometry to the sciences |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81V25 | Other elementary particle theory in quantum theory |
