Mathematical Physics

   

Diamond Operator as a Spinless Square Root of d' Alembertian

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. We found another 4 x 4 complex differential matrix as a spinless square root of d' Alembertian, which we call diamond operator. The extended Maxwell's equations including charge creation-annihilation field and the linear gravitational field equations including energy creation-annihilation field can be simply written by using the diamond operator. It is shown that the linear gravitational field equations derive Klein-Gordon equation, time independent Schrödinger equation, and the principle of quantum mechanics.

Comments: 5 Pages.

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Submission history

[v1] 2017-08-03 09:30:29
[v2] 2017-08-04 07:06:47

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