Galilei Group, Quantum Mechanics, Neutron-Proton Majorana Interaction, and Dark Matter

The Galilei symmetry demands a Bargmann Superselection rule which shows that in nonrelativistic quantum mechanics, it is impossible to have states which are linear superposition of states describing particles of different masses. We show that these kind of masses can not be the masses of particles as obtained in the nonrelativistic limiting case of the Lorentz transformation with v  c, and in which the nonrelativistc and relativistic quantum mechanical structures are related to each other. In addition, the nonrelativistic quantum mechanical structure of the Bargmann-Superselection-rule kind, has no relativistic counterpart at all. These mathematical conclusions are consolidated by the fact that there exists a Majorana interaction between each neutron-proton pair in nuclei. This Majorana interaction, for the Galilei symmetry to hold, demands that these masses be equal M n = M p . Hence there do exist two independent and simultaneous nonrelativistc quantum mechanical strucutres in nature. The Majorana interaction besides ignoring spin, neglects all the three forces - the strong, the electromagnetic and the weak. Having only space exchange allowed in it, it is a pure quantum mechanical force. Thus the mass here is pure gravitational, and which is immune to the other three forces. This makes an amazing connection between the gravitational force and quantum mechanics. This pure gravitational mass would manifest itself as the Dark Matter of the universe.