ar X iv : h ep - t h / 00 05 03 9 v 1 4 M ay 2 00 0 Clifford statistics

We formulate a real quantum theory with an orthogonal group, broken by an approximate i operator, supposed to underlie the present complex quantum theory, with its unitary group. A real quantum theory requires a real quantum statistics. We put forward a general concept of linear statistics that embraces the usual complex tensorial statistics (Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein), the nonabelions of Read and Moore, the 2-valued spinorial statistics of Wilczek, here called complex Clifford statistics, and a real Clifford statistics that we propose for elementary quantum events. We apply Clifford statistics to quanta here. A toy complex-Clifford model has the energy spectrum of a system of spin-1/2 particles in an external magnetic field. This supports the proposal that the complex double-valued rotations — spin — seen at the quantum level of resolution arise from real doublevalued permutations — swap — to be seen at higher (ultra-quantum) resolution. A toy based on real Clifford statistics shows how an imaginary unit i can arise naturally within a real theory. PACS numbers: 03.65.Bz, 03.65.Fd