Mathematical Physics


Diamond Operator as a Square Root of D'alembertian for Bosons

Authors: Hideki Mutoh

Dirac equation includes the 4 x 4 complex differential operator matrix, which is one of square roots of d'Alembertian with spin of half integer. We found another 4 x 4 complex differential matrix as a square root of d'Alembertian for bosons, which we call diamond operator. The extended Maxwell's equations with charge creation-annihilation field and the linear gravitational field equations with energy creation-annihilation field can be simply written by using the diamond operator. It is shown that the linear gravitational field equations derive Newton's second law of motion, Klein-Gordon equation, time independent Schrödinger equation, and the principle of quantum mechanics.

Comments: 6 Pages.

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Submission history

[v1] 2017-08-03 09:30:29
[v2] 2017-08-04 07:06:47
[v3] 2017-09-17 22:28:49
[v4] 2018-05-26 01:00:37

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