## Yang-Mills Field from Quaternion Space Geometry, and Its Klein-Gordon Representation

**Authors:** Alexander Yefremov, Florentin Smarandache, V. Christianto

Analysis of covariant derivatives of vectors in quaternion (Q-) spaces performed
using Q-unit spinor-splitting technique and use of SL(2C)-invariance of quaternion
multiplication reveals close connexion of Q-geometry objects and Yang-Mills (YM)
field principle characteristics. In particular, it is shown that Q-connexion (with
quaternion non-metricity) and related curvature of 4 dimensional (4D) space-times
with 3D Q-space sections are formally equivalent to respectively YM-field potential
and strength, traditionally emerging from the minimal action assumption. Plausible
links between YM field equation and Klein-Gordon equation, in particular via its
known isomorphism with Duffin-Kemmer equation, are also discussed.

**Comments:** 9 pages

**Download:** **PDF**

### Submission history

[v1] 6 Mar 2010

**Unique-IP document downloads:** 43 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*