From Standard Representations to a Global Representation with a N-Dimensional Metric in Quantum Theory

In this paper we discuss the several standard representations of Quantum Theory. The requirements of time order and operator self-adjointness are too much restrictive. To describe quantum correlations of N particles with a possible not causal order we propose a new formalism which include all conjugate quantities in the same configuration space where we define a "global state function" Ψ of 6N+1 scalar variables.

The function Ψ is 3N-dimensional (non relativist Ψ) or 4N-dimensional (relativist Ψ) when spin variables are separable. Usual kinematic functions are computed as implicit functions, and new quantum operators are introduced.