Archives for April, 2026
Why are the observable operators in QM required to be Hermitian?
Overview In quantum mechanics, observables (like position, momentum, energy) are represented by operators. Requiring those operators to be Hermitian (more precisely, self-adjoint) is not arbitrary—it follows from a few fundamental…
The unconnected manifold versus the affine connected manifold – describe what these are. Densities, Derivatives, Integrals, Invariant Derivatives in particular
This is a deep and beautiful distinction—one that sits right at the boundary between pure geometry and physics-ready geometry. Let’s build it cleanly and intuitively, then connect it to densities,…