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One attractive interpretation of quantum mechanics is the ensembleinterpretation, where Quantum Mechanics merely describes a statistical ensembleof objects and not individual objects. But this interpretation does not addresswhy the wave-function plays a central role in the calculations ofprobabilities, unlike most other interpretations of quantum mechanics. On theother hand, Classical Statistical Field Theory suffers from severe mathematicalinconsistencies (specially for Hamiltonians which are non-polynomial in thefields, e.g. General relativistic statistical field theory). We claim that bothproblems are related to each other and we propose a solution to both. We prove:1) the wave-function is a parametrization of any probability distribution of astatistical ensemble: there is a surjective map from an hypersphere to the setof all probability distributions; 2) for a quantum system defined in a2-dimensional real Hilbert space, the role of the (2-dimensional real)wave-function is identical to the role of the Euler's formula in engineering,while the collapse of the wave-function is identical to selecting the real partof a complex number; 3) the collapse of the wave-function of any quantum systemis a recursion of collapses of 2-dimensional real wave-functions; 4) thewave-function parametrization is key in the mathematical definition ofClassical Statistical Field Theory we propose here. The same formalism isapplied to Quantum Yang-Mills theory and Quantum Gravity in another article.

Relating the wave-function collapse with Euler's formula, with applications to Classical Statistical Field Theory