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We propose a new quantum approach for describing a system of $n$ interactingparticles with variable mass connected by an unknown field with variable form($n$-VMVF systems). Instead of assuming any particular nature for variation ofthe masses and field, we propose to find them from the laws that rule thedynamic of the systems. In this context, we consider masses and field arefunctions depending only on the particle positions and velocities, excludingthe presence of hidden variables. The quantum approach follows the modernmethod for constructing the quantum theory where quantum states are definedover a Hilbert space, and the operators are obtained from the canonicaltransformations of the corresponding classical theory. The classical theoryresults on two sets of second-order Hamilton constrained equations, while theHilbert space is defined over the extension of the complex number, which isdone from an unsolvable equation on the complex domain. This new approach doesnot contradict the existing theoretical theories in Particle Physics.

A new proposal for a quantum theory for isolated n-particle systems with variable masses connected by a field with variable form