nLab classical observable

Idea

In physics, an observable in the context of classical mechanics/classical field theory and in fact also in prequantum field theory is called a classical observable.

In symplectic geometry/geometric prequantum theory?, classical observables are functions on phase space, often called Hamiltonian functions. They form the Poisson algebra of classical/prequantum observables, wih the Poisson bracket Lie algebra structure.

In higher prequantum field theory these observables are refined to Hamiltonian forms/local currents and form the Poisson-bracket Lie n-algebra of local observables.

Related concepts

	classical mechanics	semiclassical approximation	…	formal deformation quantization	quantum mechanics
order of Planck's constant $\hbar$	$\mathcal{O}(\hbar^0)$	$\mathcal{O}(\hbar^1)$	$\mathcal{O}(\hbar^n)$	$\mathcal{O}(\hbar^\infty)$
states	classical state	semiclassical state			quantum state
observables	classical observable				quantum observable