There is a theory that goes by the name Margenau’s Theory, which tries its hand at reducing human consciousness to a field of probabilities in what is termed a Fock Space, which is an algebraic construction in quantum mechanics to construct the quantum states space of a variable or an unknown number of identical particles from a single particle Hilbert Space, H.
Hilbert space extends the notion of Euclidean geometry from a two-dimensional space to a three-dimensional space, and is talked about as an abstract vector space possessing the structure of an inner product that allows the length and the angle to be measured. Now, such a space could be created by an electrical activity at the synaptic level. Normal behaviour could therefore be seen as the elasticity of the field, and free will as a rupture within it. But, in what topology begs the question? Since, there is nothing in the natural topography of Hilbert Spaces that could be the generator of free will….
Three states of the Hilbert space of the quantum dimer model. There are off-diagonal matrix elements in the effective Hamiltonian which connect state ͑ a ͒ to state ͑ b ͒ , and state ͑ a ͒ to state ͑ c ͒ , by a resonance between pairs of horizontal and vertical dimers around a plaquette. The latter matrix element differs from the former because only the latter has a diagonal link across the resonating plaquette. Also shown are the corresponding values of the heights h a on the sites of the dual lattice. Credit