  We propose a new quantum approach for describing a system of $n$ interacting
particles with variable mass connected by an unknown field with variable form
($n$-VMVF systems). Instead of assuming any particular nature for variation of
the masses and field, we propose to find them from the laws that rule the
dynamic of the systems. In this context, we consider masses and field are
functions depending only on the particle positions and velocities, excluding
the presence of hidden variables. The quantum approach follows the modern
method for constructing the quantum theory where quantum states are defined
over a Hilbert space, and the operators are obtained from the canonical
transformations of the corresponding classical theory. The classical theory
results on two sets of second-order Hamilton constrained equations, while the
Hilbert space is defined over the extension of the complex number, which is
done from an unsolvable equation on the complex domain. This new approach does
not contradict the existing theoretical theories in Particle Physics.
