Noncommutative minkowski space and transcendental calculus

Appropriate choice of ordered expressions of the Weyl algebra provides us a useful transcendental calculus [Ref. 14)]. Analysing star exponential functions of quadratic forms leads us matrix representations naturally. We develop a previous calculus in Ref. 14) to construct an ordered Lie group with an adjoint invariant Lorentz metric and various interesting matrix representations according to orderings.