Qubit Mellin Transform Generation of Prime Number Product

It is interesting to think of integral transforms and their Hamiltonian and partition function space representation in quantum mechanics. When one has the phase shift scattering picture of Dirac developing concepts of modified states in the multi-dimensional Bloch sphere (more than two states for example), the result resembles the operator acting on a state. The form of this operator is usually a Hamiltonian, or an energy operator, which manipulates the energy levels of the multi-body quantum system, which is now hypothesized in the Mellin transformation case to be a Bose-Einstein distribution. Similar Hamiltonian transforms, like Fourier, Laplace, or Hadamard are basically also phase shifting the states to make new qubit outputs. What is interesting in the case of the Mellin transform, is that when the operator is a Mellin gate (hypothetical) the partition function or many-body quantum ensemble can be re-expressed as a Riemann zeta function, which is directly related to the distribution of prime numbers. These prime numbers are critical for electronic message encryption in the modern era. General Physics' scientists are working on developing a prime number based correction to amplitude function geodesic landscape string theory and, in essence, a modified fundamental theorem of calculus that involves a zeta function to correct for the turbulent nature of the decoherence of the macroscopic world. Of course, momentum dependent momentum uncertainty is a phase space fractal self-similar scale invariant law that might indicate fundamental contradictions to classical analytic determinism.

The Mellin gate, in any case, must be the issue. It is possible to use the Mellin transform to generate a Riemann zeta function. Although not easy to classically connect to a logic transistor based computer system, the output of a Mellin Hamiltonian acting on the Bose-Einstein distribution partition function will generate the zeta which can be rewritten as a product of primes. General Physics is working more to develop the qubit concept and will write more about it in the future.