Research Article

Fred Y Ye

## Abstract

A mathematical cliff consists of scalar, vector and spinor, while scalar, vector and spinor are cliff components. It is found that the static exchange product of cliff components produces quantum, such as exchange multiplication of scalar and vector [X, Y]=XY–YX = Ã¢Â„Â/i, and that the complex dynamic distribution of i(z) as logarithm of negative numbers is just probability density, yielding quantum statistical mechanism. The mathematical principle reveals physical implications characterized by static “one cliff, one state” and dynamic “i(z) generates probability”, where the complex conjugation of the cliff indicates entangled one, resembling a concise mathematical principle of quantum mechanism. While the inner relations among scalars, vectors and spinors reveal local laws, the outer relations between cliffs describe global laws, leading to harmonic mathematical physics.