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## Main Question or Discussion Point

In practical terms, what quantum theories can be applied to the mediating forces of interacting particles so as to permit degrees of freedom in excess of 3D space?

For example, could an inner product of scattering theory be extended to a higher dimension of Hillbert space so as to define virtual potential fields?

For example, could an inner product of scattering theory be extended to a higher dimension of Hillbert space so as to define virtual potential fields?