XXXVII Max Born International Symposium, Noncommutative Geometry, Quantum Symmetries and Quantum Gravity II, Faculty of Physics and Astronomy, Wroclaw University, Poland (Supported by the European Union Framework Programme Horizon 2020) (
2016)
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Abstract
This article is a summary of an expanded version of my previous publication Ref. [ 1 ]. In particular, in Ref. [1] using a new axiomatic matrix approach – which has been formulated on the basis of ring theory and Clifford algebra – by first quantization (followed by a basic procedure of minimal coupling to the space-time geometry) of a special relativistic algebraic matrix equation, a certain massive form of gravitational field equations – with new matrix formalism and also a definite form of torsion which generates the gravitational field's invariant mass – is derived uniquely. It is shown that the massless case of these derived equations is equivalent to the Einstein field equations (including a cosmological constant). Moreover, it has been shown that the matrix formalism of derived gravitational field equations, is compatible with matrix representations of certain Clifford algebras.