From the Spontaneous Mirror Symmetry Violation to the Differential Mass Operator

The unidenticality of lifetimes $\tau_{s}$ and space-time coordinates $(t_{s}, {\bf x}_{s})$

of left $(s=L=-1)$ and right $(s=R=+1)$ types of elementary objects establishes, as was noted

by the author in [1,2] for the first time, the full spin structure of all equations of motion

in a truly quantum theory of particles with a nonzero spin in which the mass $m_{s},$ energy

$E_{s},$ and momentum ${\bf p}_{s}$ are predicted as the matrices

$$m_{s}={{m_{V} \, \, \, \, 0}\choose{\ 0 \, \, \, \, \ m_{V}}}, \, \, \, \,

E_{s}={{E_{V} \, \, \, \, 0}\choose{\ 0 \, \, \, \, \ E_{V}}}, \, \, \, \,

{\bf p}_{s}={{{\bf p}_{V} \, \, \, \, 0}\choose{\ 0 \, \, \, \, \ {\bf p}_{V}}},

\eqno(1)$$

$$m_{V}={{m_{L} \, \, \, \, 0}\choose{\ 0 \, \, \, \, \ m_{R}}}, \, \, \, \,

E_{V}={{E_{L} \, \, \, \, 0}\choose{\ 0 \, \, \, \, \ E_{R}}}, \, \, \, \,

{\bf p}_{V}={{{\bf p}_{L} \, \, \, \, 0}\choose{\ 0 \, \, \, \, \ {\bf p}_{R}}},

\eqno(2)$$

where $V$ must be accepted as an index of a distinction.

Such a possibility is realized owing to the spontaneous mirror symmetry violation. Thereby, it expresses the ideas about that $m_{s}$ similarly to each of $E_{s}$ and ${\bf p}_{s}$ comes forward

in the same space-time, where they exist, as the one of its following differential operators:

$$m_{s}=-i\partial_{\tau}^{s}=-i\frac{\partial}{\partial \tau_{s}}, \, \, \, \,

E_{s}=i\partial_{t}^{s}=i\frac{\partial}{\partial t_{s}}, \, \, \, \,

{\bf p}_{s}=-i\partial_{\bf x}^{s}=-i\frac{\partial}{\partial {\bf x}_{s}}.

\eqno(3)$$

We discuss a theory in which an wave function is defined at the new level, namely, at the level

of the unity of differential operators (3) as a mirrorly wave function. This connection requires

one to derive all equations of a truly quantum theory of fermions, bosons, and atoms from the point of view of the mass-charge structure [3,4] of gauge invariance including a unified theoretical description of all types of forces as the structural components of the same allgravity [5] responsible for all that in a curved space-time.