Thus, is absolutely gauge-invariant, and may be related to physical observables.

In particular, certain physical observables, such as the area, have a discrete spectrum.

This equation shows that, given quantum characteristics are constructed, physical observables can be found without further addressing to Hamiltonian.

As such, quantum logic provides a unified and consistent mathematical theory of physical observables and quantum measurement.

In quantum mechanics, physical observables are represented mathematically by linear operators on Hilbert spaces.

Usually this vector basis is chosen to reflect some symmetry of the space-time, leading to simplified expressions for physical observables.

Heuristically, in quantum field theory one is interested in the result of physical observables represented by operators.

It is generally believed that C*-algebras were first considered primarily for their use in quantum mechanics to model algebras of physical observables.

Just hold onto the idea that certain operators will possess mathematical properties which make them perfectly suited to the role of representing physical observables.

Other physical observables diverge at this point, leading to some confusion at the beginning.