The abstract theory establishes that a stable quantum vacuum with zero lowest energy requires all fermions to possess positive energy, necessitating Dirac's interpretation where the negative-energy state is filled by Pauli Exclusion Principle-allowed particles while boson states remain empty due to lack of exclusion. Furthermore, it formalizes the Heisenberg Uncertainty Principle as a mathematical consequence of non-commuting position and momentum operators ($\Delta x \Delta p \geq \hbar/2$), derived via integration by parts within the Hilbert space framework, which dictates that precise knowledge of one variable precludes simultaneous precision in its conjugate pair.
The abstract theory establishes that a stable quantum vacuum with zero lowest energy requires all fermions to possess positive energy, necessitating Dirac's interpretation where the negative-energy s…