## Algebraic Field Theory-a Mathematical Construction of the Vacuum

**Authors:** Robert H Ihde

All algebras of quantum theory are algebras over a field or briefly K-algebras of a binary operation, which are defined as constant invariants over the Poincaré group. The Christoffel symbols occurring in the classical geodetic equation can be understood as a representation of a K-algebra. In contrary to the constant algebras of quantum theory, the K-algebra of the Christoffel symbols is a function of space-time. A mathematical, conformal unification of geometry and algebra requires a corresponding dependence on space-time for the quantum algebras. Assuming the existence of an algebraic field, based on a changing binary operation with a feedback to the domain, a quantum mechanical vacuum equation for gravity is established. The vacuum equation structurally follows a generalized, pseudo-linear Dirac-Maxwell system with additional algebraic constraints. A physical existence of the algebraic field, as the counterpart to the geometric field of gravity, can be falsified by the experiment. The part of the spin in the magnetic moment of a particle would then depend on its acceleration, since the algebraic field should influence the spin algebra accordingly.

**Comments:** 22 Pages. Some error corrections.

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### Submission history

[v1] 2018-08-31 15:39:49

[v2] 2018-09-20 14:32:20

[v3] 2018-09-25 12:15:08

[v4] 2018-10-07 12:04:39

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